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Motion

邊玩邊學

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給老師： 為 Motion（Physics、CIE）準備好可直接使用的課程投影片, 複習筆記, 圖表——用於你的課程，或把這個主題當成互動班級活動，讓學生以即時遊戲的方式進行。

課程筆記

Speed & Velocity

  • Speed = distance travelled per unit time; a scalar quantity (magnitude only).
  • Equation: v = \frac{s}{t}, where v in m/s, s in m, t in s.
  • Average speed = total distance / total time; useful when speed varies.
  • Velocity = speed in a given direction; a vector quantity (magnitude and direction).
  • Velocity uses displacement (vector) instead of distance.
  • Same speed but different directions → different velocities.

A person walking at 2.0 m/s and a bee flying at 4.5 m/s, illustrating speed.

A person walking at 2.0 m/s and a bee flying at 4.5 m/s, illustrating speed.

Acceleration (Extended)

  • Acceleration = rate of change of velocity; a = \frac{\Delta v}{\Delta t}, units m/s².
  • Change in velocity: \Delta v = v - u (final minus initial).
  • Positive acceleration = speeding up; negative acceleration (deceleration) = slowing down.
  • Any change in velocity (speed up, slow down, change direction) is acceleration.
  • Formula triangle: cover the quantity to find; a = \frac{\Delta v}{\Delta t}, \Delta v = a \times \Delta t, \Delta t = \frac{\Delta v}{a}.

Examples of positive and negative acceleration

Examples of positive and negative acceleration

Distance-Time Graphs

  • Distance-time graph: straight line = constant speed; horizontal line = stationary.
  • Gradient = speed; steeper slope = faster speed.
  • Curved line = changing speed (acceleration/deceleration); increasing gradient = speeding up, decreasing = slowing down.
  • To calculate speed: draw a large gradient triangle, find \frac{\Delta y}{\Delta x}.
  • Always check units (e.g., km → m, min → s).

The gradient of a distance-time graph, found from the change in distance (Δy) over the change in time (Δx), gives the speed.

The gradient of a distance-time graph, found from the change in distance (Δy) over the change in time (Δx), gives the speed.

Speed-Time Graphs

  • Speed-time graph: straight line = constant acceleration; horizontal line = constant speed (zero acceleration).
  • Gradient = acceleration; positive gradient = acceleration, negative = deceleration.
  • Area under graph = distance travelled.
  • Split area into triangles and rectangles: triangle area = \frac{1}{2}bh, rectangle area = bh.
  • Total distance = sum of all areas under the line.

The area under a speed-time graph, split into a triangle and a rectangle (base × height), gives the distance travelled.

The area under a speed-time graph, split into a triangle and a rectangle (base × height), gives the distance travelled.

Calculating Acceleration from Speed-Time Graphs (Extended)

  • For constant acceleration: gradient = \frac{\Delta v}{\Delta t} using a straight line.
  • For changing acceleration: draw a tangent at the point; gradient of tangent = instantaneous acceleration.
  • A tangent is a straight line that just touches the curve at that point.
  • Use a large gradient triangle on the tangent to calculate \frac{\Delta y}{\Delta x}.

A tangent drawn to a curved speed-time graph at a point gives the gradient, and so the instantaneous acceleration, at that point.

A tangent drawn to a curved speed-time graph at a point gives the gradient, and so the instantaneous acceleration, at that point.

Freefall

  • In absence of air resistance, all objects fall with same acceleration: g = 9.8 \, \text{m/s}2 (acceleration of freefall).
  • Weight W = mg, where g is gravitational field strength (N/kg).
  • With air resistance: forces are weight (down) and air resistance (up).
  • Air resistance increases with speed; when it equals weight, resultant force = 0 → terminal velocity.
  • Skydiver: initially accelerates, then air resistance increases, eventually reaches terminal velocity; deploying parachute increases air resistance → deceleration to a lower terminal velocity.
  • In a vacuum (no air resistance), objects never reach terminal velocity; they accelerate at g continuously.

A person dropping two objects of different sizes from the Leaning Tower of Pisa to demonstrate freefall.

A person dropping two objects of different sizes from the Leaning Tower of Pisa to demonstrate freefall.

投影片

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練習題

免費預覽——63 題中的 8 題。註冊即可查看全部。

  1. 1.Which of the following is a scalar quantity?

    Easy
    • Avelocity
    • Bdisplacement
    • Cacceleration
    • Dspeed

  2. 2.What is the acceleration of free fall near Earth's surface?

    Easy
    • A9.8 m/s
    • B9.8 m/s²
    • C9.8 m/s² downward
    • D9.8 N/kg

  3. 3.On a distance-time graph, a horizontal line indicates that the object is:

    Easy
    • Aaccelerating
    • Bmoving at constant speed
    • Cstationary
    • Ddecelerating

  4. 4.Which of the following is the correct definition of velocity?

    Easy
    • ADistance travelled per unit time
    • BSpeed in a given direction
    • CChange in displacement per unit time
    • DRate of change of speed

  5. 5.The area under a speed-time graph represents:

    Easy
    • Aacceleration
    • Bvelocity
    • Cdistance travelled
    • Ddeceleration

  6. 6.An object accelerates from 4 m/s to 10 m/s in 3 s. What is its acceleration?

    Medium
    • A2 m/s²
    • B3 m/s²
    • C4 m/s²
    • D6 m/s²

  7. 7.On a speed-time graph, a straight line with negative gradient represents:

    Easy
    • Aconstant acceleration
    • Bconstant deceleration
    • Cconstant speed
    • Dincreasing acceleration

  8. 8.A skydiver falls from a plane. After reaching terminal velocity, the parachute opens. Which statement is correct?

    Medium
    • AThe skydiver immediately stops falling.
    • BThe skydiver accelerates upward.
    • CThe skydiver decelerates to a lower terminal velocity.
    • DThe skydiver continues at the same terminal velocity.

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