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3.1Accelerated Motion

Acceleration — American System Physics Revision Notes & Topical Questions

10 min read 7 parts Lesson 3 of 5 1 quiz

📚 American System Physics Hub / Topical Revision
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Lesson summary

Define acceleration and calculate average acceleration.Acceleration = change in velocity ÷ time takena = Δv/Δt = (vf − vi)/Δt (m/s2).Rearrangedvf = vi + aΔt; Δt = (vf − vi)/a.Acceleration = gradient of velocity–time graph.Displacement = area under velocity–time graph (triangle = …

  • A velocity–time graph is the key tool
  • A falling object with air resistance
  • A car increases its velocity from 8.0 m/s to 26 m/s in 6.0 s. Find its acceleration
  • Instantaneous acceleration
  • Constant (uniform) acceleration
  • Deceleration

Section 1 of 7Acceleration

Essential knowledge
3.1 Acceleration concept map: Acceleration = change in velo, Rearranged, A velocity–time graph is the, A falling object with air res, A car increases its velocity
Visual guide to the key ideas explained in this lesson.
An object accelerates whenever its velocity changes — by speeding up, slowing down or changing direction.
In a motion diagram, acceleration is shown by changing spacing between dots; velocity-change vectors Δv (drawn from one velocity arrow to the next) point in the direction of acceleration.
Average acceleration is Δv/Δt. The unit m/s2 means "metres per second, per second".
A velocity–time graph is the key tool
A velocity–time graph is the key tool gradient gives acceleration; a straight line means constant acceleration; a curve means changing acceleration.
The area between the v–t graph and the time axis gives displacement. Split complex shapes into rectangles and triangles.
Acceleration being negative does not always mean slowing down: an object moving in the negative direction with negative acceleration is speeding up.
Deceleration is the everyday word for slowing down; give its magnitude in m/s2.
Instantaneous acceleration at a point on a curved v–t graph is the gradient of the tangent at that point.
A falling object with air resistance
A falling object with air resistance acceleration starts at about 9.8 m/s2, decreases as air resistance increases, and becomes zero at terminal velocity (the v–t graph curves and levels off).
A car moving around a bend at constant speed is accelerating because its direction of motion changes.

Section 2 of 7Process & sequence

1
Set up a trolley on a ramp with two light gates a measured distance apart (or a single double-card gate).
2
Release the trolley from rest and record the speed at each gate (card length ÷ blocked time).
3
Record the time taken to travel between the gates.
4
Calculate acceleration: a = (v2 − v1)/Δt.
5
Repeat for several releases and take a mean.
6
Change the ramp angle (independent variable) and repeat to investigate how acceleration depends on slope.

Analysing a velocity–time graphwrite these steps in this order; each step is a marking point.

1
Identify each straight section of the graph and its time interval.
2
For each section, calculate the gradient (Δv/Δt) to find acceleration.
3
Note sections where the gradient is zero (constant velocity).
4
Split the area under the graph into rectangles and triangles.
5
Add the areas to obtain total displacement, and divide by total time for average velocity.

Section 3 of 7Compare

Signs of velocity and acceleration (+ = right)
vaMotion
++Moving right, speeding up
+−Moving right, slowing down
−−Moving left, speeding up
−+Moving left, slowing down
any0Constant velocity
Reading a velocity–time graph
FeatureMeaning
Horizontal lineConstant velocity (a = 0)
Straight line sloping upConstant positive acceleration
Straight line sloping downConstant negative acceleration
CurveChanging acceleration
Line on time axisAt rest
Area under graphDisplacement

Section 4 of 7Worked examples

A car increases its velocity from 8.0 m/s to 26 m/s in 6.0 s. Find its acceleration.

  • a = (vf − vi)/Δt = (26 − 8.0)/6.0 = 18/6.0 = 3.0 m/s2.
24 m
A cyclist travelling at 12 m/s brakes to rest in 4.0 s. Find the acceleration and the distance travelled while braking.
  • a = (0 − 12)/4.0 = −3.0 m/s2 (deceleration 3.0 m/s2).
    • Distance = area of triangle under v–t graph = ½ × 4.0 × 12 = 24 m.
1600 m
A v–t graph shows a train accelerating uniformly from 0 to 20 m/s in 40 s, then moving at 20 m/s for 60 s. Find the total displacement.
  • Triangle
    • ½ × 40 × 20 = 400 m.
    • Rectangle: 60 × 20 = 1200 m.
    • Total = 1600 m (1.6 × 103 m).

Section 5 of 7Key terms

Section 6 of 7Command terms

Command terms
Identify / Describe (FRQ)
A short, specific statement; describing requires relevant characteristics, not a single word.
Explain / Justify (FRQ)
Give the cause-and-effect reasoning or evidence; a restated fact does not score.
Calculate
Show setup, substitution and the answer with units.
Predict
State the expected outcome; add a reason only if asked to justify.
MCQ technique
Read every option; eliminate distractors that are true statements but do not answer the question; watch for NOT/EXCEPT.

Section 7 of 7Exam technique

Keywords the mark scheme looks for in this lesson

Keywords the mark scheme looks for in this lesson
Acceleration · Average acceleration · Instantaneous acceleration · Constant (uniform) acceleration · Deceleration · Velocity–time graph · Change in velocity · Initial velocity · Final velocity · Non-uniform motion · Terminal velocity · Speeding up / slowing down rule
Learn each definition in the Key words tab exactly; a missing keyword in a definition usually loses the mark.

How to get full marks (examiner guidance)

1
Answer exactly what is asked; extra correct material does not earn credit, and contradictory statements can cancel credit (AP FRQ).
2
Use precise vocabulary, never “it/stuff/things”.
3
Show units and working in calculations.
4
In MCQs, predict the answer before reading the options, then eliminate.

Words to avoid

1
acceleration is how fast something goesacceleration is the rate of change of velocity.
2
constant speed means no accelerationconstant velocity means no acceleration; changing direction at constant speed is acceleration.
3
negative acceleration always means slowing downan object slows down when its acceleration is opposite to its velocity.
4
the unit of acceleration is m/sm/s2.
5
the area under a v–t graph is the accelerationthe gradient is the acceleration; the area is the displacement.

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