Kinematics

Học bằng cách chơi

Trả lời những câu hỏi này để kiếm năng lượng, rồi câu cá và khám phá. Không cần tài khoản.

Dành cho nhà giáo dục: slide bài học, ghi chú ôn tập sẵn dùng cho Kinematics (Physics, HL) — dùng trong bài giảng của bạn, hoặc chạy chủ đề như một hoạt động lớp học tương tác để người học chơi như một trò chơi trực tiếp.

Ghi chú bài học

Distance & Displacement

Distance is a measure of how far an object travels; it is a scalar quantity, so direction is not important.
Displacement is a measure of how far something is from its starting position, along with its direction; it is a vector quantity.
Displacement is the change in position and describes both magnitude and direction.
For a 300 m race on a 400 m track, the distance travelled is 300 m, but the displacement is 100 m to the right.
If athletes run the full 400 m lap, their final displacement is zero because they finish at the starting point.
When travelling to school, the distance includes all twists and turns, while the displacement is a straight line from home to school.

Distance vs displacement

Speed & Velocity

Speed is the distance an object travels every second; it is a scalar quantity.
Average speed is calculated as: average speed = total distance ÷ time taken.
Velocity is the rate of change of displacement; it is a vector quantity because it has both magnitude and direction.
Velocity is speed in a given direction, so it can be negative (e.g., a ball thrown upwards at 3 m s⁻¹ comes down at –5 m s⁻¹ if upwards is positive).
Instantaneous speed (or velocity) is the speed (or velocity) at a given point in time; on a displacement-time graph, it is found by drawing a tangent and calculating its gradient.
Average velocity is calculated as: v̄ = Δs / Δt, where Δs is total displacement and Δt is total time.
If acceleration is constant and initial velocity u and final velocity v are known, average velocity can also be calculated as v̄ = (u + v) / 2.

Comparing speed and velocity

Acceleration

Acceleration is defined as the rate of change of velocity; it is a vector quantity measured in metres per second squared (m s⁻²).
Average acceleration is calculated as: a = Δv / Δt, where Δv = v – u (final velocity minus initial velocity).
Instantaneous acceleration is the acceleration at a given point in time; on a velocity-time graph, it is the gradient at that point.
If an object is speeding up, its acceleration is positive; if it is slowing down, its acceleration is negative (deceleration).
Acceleration can also be negative if the object is accelerating in the negative direction.
A curved line on a velocity-time graph indicates changing (non-uniform) acceleration.

Illustration of positive and negative acceleration with a rocket and a car.

Kinematic Equations

The kinematic equations (often called SUVAT equations) describe motion with constant (uniform) acceleration.
The five variables are: s = displacement, u = initial velocity, v = final velocity, a = acceleration, t = time interval.
The four kinematic equations are: v = u + at, s = ut + ½at², v² = u² + 2as, and s = (u + v)t / 2.
These equations are given in the data booklet, so you do not need to memorise them.
Key phrases: 'starts from rest' means u = 0; 'falling due to gravity' means a = g = 9.8 m s⁻² (positive if downwards is positive, negative if upwards is positive).
To solve problems: list known and unknown quantities, choose the equation containing those quantities, convert units to SI, then substitute and solve.
Always choose a single direction as positive and stick with it throughout the question to avoid sign errors.

Motion Graphs

On a displacement-time graph: slope equals velocity; a straight diagonal line represents constant velocity; a curved line represents acceleration; a horizontal line represents rest.
On a velocity-time graph: slope equals acceleration; a straight diagonal line represents uniform acceleration; a curved line represents non-uniform acceleration; a horizontal line represents constant velocity.
The area under a velocity-time graph equals the change in displacement.
On an acceleration-time graph: the area under the curve equals the change in velocity; a horizontal line represents constant acceleration.
For a bouncing ball (ignoring air resistance), acceleration due to gravity is always constant and directed downwards.
At the highest point of a bounce, the ball momentarily has zero velocity, and its velocity changes from positive to negative.
At the lowest point (ground), velocity changes instantaneously from negative to positive, but speed remains the same.

Motion on a speed–time graph

Projectile Motion

A projectile is a particle moving freely (non-powered) under gravity in a two-dimensional plane; examples include a thrown ball or a cannonball.
Assumptions: fluid resistance is negligible, and acceleration due to free-fall g is constant near Earth's surface.
The horizontal and vertical components of motion are independent of each other and must be evaluated separately using SUVAT equations.
Horizontal component: velocity is constant, acceleration is zero, and displacement is maximum range at the end of motion.
Vertical component: velocity is zero at maximum height, acceleration is g = 9.8 m s⁻² (positive downwards, negative upwards).
For a projectile launched at speed u and angle θ to the horizontal: vertical component = u sinθ, horizontal component = u cosθ.
Time to maximum height is half the total time of flight; maximum height occurs when vertical velocity = 0.
Projectile motion is typically symmetrical when air resistance is ignored, so total time or range can be found by doubling the value from start to peak.

Fluid Resistance

Fluid resistance refers to the effects of gases and liquids on the motion of a body; these resistive forces are known as viscous drag (or air resistance).
Frictional forces always act opposite to motion, never speed an object up, and transfer energy away from the object to the surroundings.
Lift is an upward force on an object moving through a fluid, perpendicular to the fluid flow (e.g., air pushing up on aeroplane wings).
Drag forces increase with the speed of the object.
In projectile motion, air resistance decreases time of flight, horizontal velocity, and range, and increases horizontal deceleration.
With air resistance, the trajectory is no longer a parabola; it is steeper on the way down than on the way up.
For sports like long jump or javelin, an optimum angle against air resistance is used to produce the greatest range.

Air resistance is a type of drag: it opposes motion through a fluid and heats the object.

Terminal Speed

For a body in free fall in a vacuum, the only force is weight, and acceleration is g due to gravity.
As a body falls through a fluid, viscous drag increases with speed, so the resultant force and acceleration decrease (F = ma).
Terminal velocity is reached when the viscous drag force equals the weight; the body then falls at a constant velocity with zero acceleration.
Terminal velocity can occur for objects falling through a gas or a liquid.
On a velocity-time graph for a skydiver, acceleration (gradient) decreases until it becomes zero at terminal velocity.
After a parachute is deployed, the skydiver decelerates to a lower terminal velocity; they do not move upwards.
A heavier skydiver reaches a higher terminal velocity and reaches it faster than a lighter skydiver with the same surface area and volume.
If air resistance is 'negligible', it is taken to be so small that it has no effect on the motion.

A speed-time graph for a skydiver: air resistance builds as speed increases until it balances weight and a constant (terminal) velocity is reached.

Slide

Step through every slide for this topic — plus flashcards and revision notes — with a free account.

ĐĂNG KÝ — MIỄN PHÍ ĐĂNG NHẬP

Câu hỏi luyện tập

Xem trước miễn phí — 8 trên 61 câu hỏi. Đăng ký để xem tất cả.

1.Which of the following quantities is a vector?
Easy
- ADistance
- BSpeed
- CDisplacement
- DTime
2.A student walks 300 m around a curved path and ends up 100 m from the starting point. What are the distance travelled and the magnitude of the displacement?
Easy
- A300 m and 300 m
- B300 m and 100 m
- C100 m and 300 m
- D100 m and 100 m
3.A runner completes one full lap of a 200 m track in 63.4 s. What is the average speed of the runner?
Easy
- A0 m s⁻¹
- B3.15 m s⁻¹
- C6.31 m s⁻¹
- D200 m s⁻¹
4.A runner completes one full lap of a 200 m track. What is the average velocity over the entire lap?
Easy
- A3.15 m s⁻¹
- B0 m s⁻¹
- C200 m s⁻¹
- D63.4 m s⁻¹
5.Which statement correctly defines instantaneous velocity?
Medium
- AThe total displacement divided by the total time taken
- BThe velocity of an object at a particular moment in time
- CThe change in velocity divided by the time taken
- DThe total distance travelled divided by the total time taken
6.A train decelerates uniformly from 50 m s⁻¹ to 42 m s⁻¹ in 30 s. What is its acceleration?
Medium
- A+0.27 m s⁻²
- B−0.27 m s⁻²
- C−8 m s⁻²
- D−240 m s⁻²
7.A ball is thrown vertically upwards. At its highest point, what are its velocity and acceleration?
Medium
- AVelocity zero, acceleration zero
- BVelocity zero, acceleration 9.8 m s⁻² downwards
- CVelocity maximum, acceleration zero
- DVelocity zero, acceleration 9.8 m s⁻² upwards
8.On a velocity-time graph, what does the area under the curve represent?
Easy
- AAcceleration
- BDisplacement
- CSpeed
- DForce

Thêm câu hỏi

9.Which quantity is defined as the rate of change of velocity?
Easy
- ASpeed
- BDisplacement
- CAcceleration
- DDistance
10.An object is released from rest and falls freely under gravity. Which kinematic equation would you use to calculate its velocity after falling a known distance?
Medium
- Av = u + at
- Bs = ut + ½at²
- Cv² = u² + 2as
- Ds = ½(u + v)t
11.A projectile is launched at an angle θ to the horizontal with initial speed u. Which expression gives the initial vertical component of its velocity?
Medium
- Au cos θ
- Bu sin θ
- Cu tan θ
- Du / sin θ
12.In projectile motion with negligible air resistance, which statement about the horizontal component of velocity is correct?
Medium
- AIt decreases steadily as the projectile rises
- BIt remains constant throughout the flight
- CIt is zero at the maximum height
- DIt increases as the projectile falls
13.At what point in its trajectory does a projectile have zero vertical velocity?
Medium
- AAt the launch point
- BAt the maximum height
- CAt the landing point
- DIt never has zero vertical velocity
14.Which of the following is a correct statement about the acceleration of a projectile (ignoring air resistance)?
Medium
- AThe horizontal acceleration is g and the vertical acceleration is zero
- BThe horizontal acceleration is zero and the vertical acceleration is g
- CBoth horizontal and vertical accelerations are equal to g
- DBoth horizontal and vertical accelerations are zero
15.What is the effect of air resistance on the range and maximum height of a projectile compared with the same projectile in a vacuum?
Medium
- ARange increases, maximum height increases
- BRange decreases, maximum height decreases
- CRange increases, maximum height decreases
- DRange stays the same, maximum height decreases
16.A skydiver jumps from a plane and eventually reaches terminal velocity. Which statement describes the forces on the skydiver at terminal velocity?
Medium
- AThe weight is greater than the drag force
- BThe drag force is greater than the weight
- CThe drag force equals the weight, so the resultant force is zero
- DThere are no forces acting on the skydiver
17.Two skydivers, A (heavier) and B (lighter), have the same surface area and volume. Which skydiver reaches a higher terminal velocity and which reaches terminal velocity first?
Medium
- AA reaches a higher terminal velocity and reaches it first
- BB reaches a higher terminal velocity and reaches it first
- CA reaches a higher terminal velocity but B reaches it first
- DBoth reach the same terminal velocity at the same time
18.Which of the following is a correct statement about frictional forces such as viscous drag?
Easy
- AThey act in the same direction as the motion
- BThey always slow an object down or keep it moving at constant speed
- CThey speed an object up
- DThey do not transfer energy
19.Which of the following quantities are vectors? (Select all that apply.)
Medium
- ADistance
- BDisplacement
- CSpeed
- DVelocity
- EAcceleration
20.Which of the following are affected by fluid resistance in projectile motion? (Select all that apply.)
Medium
- ATime of flight
- BHorizontal velocity
- CRange
- DShape of trajectory
- EAcceleration due to gravity
21.Which of the following statements about a body falling through a fluid are correct? (Select all that apply.)
Medium
- AViscous drag increases as the body's speed increases
- BThe acceleration decreases as the body falls
- CTerminal velocity is reached when drag equals weight
- DThe body continues to accelerate indefinitely
- EThe resultant force is zero at terminal velocity
22.Which of the following are key features of a displacement-time graph? (Select all that apply.)
Medium
- AThe slope equals velocity
- BThe y-intercept equals the initial displacement
- CA straight diagonal line represents constant velocity
- DThe area under the curve equals displacement
- EA horizontal line represents a state of rest
23.Distance is a scalar quantity and displacement is a vector quantity.
Easy
True or false?
24.The acceleration of an object can be negative even when it is speeding up.
Easy
True or false?
25.On a velocity-time graph, the gradient of the line gives the acceleration.
Easy
True or false?
26.In projectile motion with no air resistance, the horizontal velocity of the projectile changes as it moves.
Easy
True or false?
27.A skydiver moves upwards when their parachute is deployed.
Medium
True or false?
28.At terminal velocity, the resultant force on a falling object is zero.
Medium
True or false?
29.The kinematic (SUVAT) equations can be used to determine the distance fallen by an object when the resultant force on it is changing.
Medium
True or false?
30.Match each quantity to whether it is a scalar or a vector.
Medium
- Distance
- Displacement
- Speed
- Velocity
- Scalar
- Vector
31.Match each graph feature to what it represents on a velocity-time graph.
Medium
- Gradient
- Area under the curve
- y-intercept
- Horizontal line
- Acceleration
- Change in displacement
- Initial velocity
- Constant velocity
32.Match each term in projectile motion to its correct definition.
Medium
- Time of flight
- Maximum height
- Range
- Vertical velocity at maximum height
- Total time in the air
- Height at which vertical velocity is zero
- Horizontal distance travelled
- Zero
33.Place the following steps in the correct order for solving a problem using the kinematic equations.
Medium
- List the known and unknown quantities
- Choose the kinematic equation containing those quantities
- Convert units to SI units
- Substitute values and solve for the unknown
34.Place the following stages of a skydiver's motion in the correct order, starting from the moment of jumping.
Medium
- Skydiver jumps and accelerates downwards
- Viscous drag increases as speed increases
- Drag equals weight and terminal velocity is reached
- Parachute deploys and skydiver decelerates to a lower terminal velocity
35.Which of the following statements about distance and displacement are correct? (Select all that apply.)
Medium
- ADistance is a scalar quantity and displacement is a vector quantity.
- BThe magnitude of displacement can never be greater than the distance travelled.
- CDisplacement includes direction, whereas distance does not.
- DIf an object returns to its starting point, its displacement is zero but the distance travelled is not zero.
- EDistance can be negative if the object moves in the negative direction.
36.Match each quantity to its correct SI unit.
Easy
- Distance
- Speed
- Acceleration
- Time
- m
- m s⁻¹
- s
37.Which of the following are correct features of a velocity–time graph? (Select all that apply.)
Medium
- AThe gradient of the line gives the acceleration.
- BThe area under the line gives the change in displacement.
- CA horizontal line represents motion with constant velocity.
- DA curved line represents uniform acceleration.
- EThe y-intercept gives the initial velocity.
38.On a displacement–time graph, a straight line with a positive slope represents an object moving with constant velocity in the positive direction.
Easy
True or false?
39.A ball is thrown vertically upwards. Which of the following statements about its acceleration is correct at all points of its motion (ignoring air resistance)?
Medium
- AThe acceleration is zero at the highest point.
- BThe acceleration is directed upwards while the ball is rising and downwards while it is falling.
- CThe acceleration is constant and directed downwards throughout the motion.
- DThe acceleration is directed downwards while rising and upwards while falling.
40.Which of the following statements about the horizontal and vertical components of projectile motion (with negligible air resistance) are correct? (Select all that apply.)
Medium
- AThe horizontal component of velocity is constant.
- BThe vertical component of velocity changes at a constant rate.
- CThe horizontal acceleration is equal to g.
- DThe vertical acceleration is equal to g downwards.
- EThe horizontal and vertical motions are independent of each other.
41.State the SI unit of acceleration.
Easy
42.State the SI unit of velocity.
Easy
43.What is the name given to the constant velocity reached by an object falling through a fluid when the drag force equals its weight?
Medium
44.A ball is projected horizontally at 27.0 m s⁻¹ from a cliff and travels a horizontal distance of 40.0 m before hitting the ground. Calculate the time of flight of the ball.
Medium
45.A ball is projected horizontally at 27.0 m s⁻¹ from a cliff and travels a horizontal distance of 40.0 m before hitting the ground. Calculate the height of the cliff. (Take g = 9.81 m s⁻².)
Medium
46.A projectile has a final horizontal velocity of 3.5 m s⁻¹ and a final vertical velocity of 3.8 m s⁻¹. Calculate the magnitude of its final velocity.
Medium
47.A stone is thrown vertically upwards with a speed of 20.0 m s⁻¹ from a point 73 m above the sea. Calculate the maximum height reached above the point it was thrown. (Take g = 9.81 m s⁻².)
Medium
48.A particle falls from rest under gravity for 0.7 m with negligible air resistance. Calculate its final velocity. (Take g = 9.81 m s⁻².)
Medium
49.Complete the definitions by filling in the blanks.
Easy
Distance is a ____ quantity, whereas displacement is a ____ quantity.
50.Complete the definition of velocity.
Easy
Velocity is defined as the rate of change of ____.
51.Complete the statement about the kinematic equations by filling in the blanks.
Medium
The kinematic (SUVAT) equations can describe the motion of an object moving with ____ acceleration in a ____ line.
52.Complete the statement about projectile motion by filling in the blanks.
Medium
In projectile motion, the horizontal and vertical components of motion are ____ of each other, and the vertical acceleration is equal to ____.
53.Describe how the fluid resistance on an object in free fall means it reaches a terminal velocity.
Medium
54.Explain why the gradient of a velocity-time graph between t = 0.0 s and t = 0.5 s for an object thrown upwards is roughly 10 m s⁻².
Medium
55.A student states that the velocity-time graph shows an object travels the same distance upwards as it does downwards. Explain how the velocity-time graph shows this.
Medium
56.State and explain whether a SUVAT equation can be used to determine the distance a block falls while the tension in an elastic rope is changing as it extends.
Medium
57.A ball is projected horizontally at 27.0 m s⁻¹ from a cliff and travels a horizontal distance of 40.0 m before hitting the ground. Calculate the time of flight of the ball.
Medium
- A1.48 s
- B3.48 s
- C2.48 s
- D0.48 s
58.A ball is projected horizontally at 27.0 m s⁻¹ from a cliff and travels a horizontal distance of 40.0 m before hitting the ground. Calculate the height of the cliff. (Take g = 9.81 m s⁻².)
Medium
- A9.8 m
- B12.8 m
- C10.8 m
- D11.8 m
59.A projectile has a final horizontal velocity of 3.5 m s⁻¹ and a final vertical velocity of 3.8 m s⁻¹. Calculate the magnitude of its final velocity.
Medium
- A5.2 m s⁻¹
- B7.2 m s⁻¹
- C4.2 m s⁻¹
- D6.2 m s⁻¹
60.A stone is thrown vertically upwards with a speed of 20.0 m s⁻¹ from a point 73 m above the sea. Calculate the maximum height reached above the point it was thrown. (Take g = 9.81 m s⁻².)
Medium
- A24.4 m
- B20.4 m
- C22.4 m
- D18.4 m
61.A particle falls from rest under gravity for 0.7 m with negligible air resistance. Calculate its final velocity. (Take g = 9.81 m s⁻².)
Medium
- A3.7 m s⁻¹
- B2.7 m s⁻¹
- C5.7 m s⁻¹
- D4.7 m s⁻¹

Unlock all 61 questions & more

Tạo tài khoản miễn phí để xem mọi câu hỏi, slide, thẻ ghi nhớ và ghi chú ôn tập cho chủ đề này.

ĐĂNG KÝ — MIỄN PHÍ ĐĂNG NHẬP

Đề thi cũ

Luyện đề thi cũ cho chủ đề này sắp ra mắt.

Sắp ra mắt