4PH1

Movement & Position

Forces & Motion · 1 question type

Practise

Exam Frequency Analysis

Past paper frequency (2018 to 2024)

This topic accounts for approximately 12% of your exam marks.

stable
High
Stable12%

Distance-time graphs, speed calculations and velocity appear in nearly every series.

Definition and equation

  • Acceleration is the rate of change of velocity, that is, how much the velocity changes each second
  • Equation:

a = Δv / t = (v − u) / t

  • where:
    • a = acceleration in metres per second squared (m/s²)
    • u = initial velocity (m/s)
    • v = final velocity (m/s)
    • t = time over which the velocity changes (s)
  • The units of acceleration, m/s², come from "change in m/s, per s", because the velocity changes by a metres per second every second

Sign of the acceleration

  • If the calculated value of a comes out positive, the object is gaining speed in the direction it is already moving (it is accelerating)
  • If the calculated value of a comes out negative, the object is losing speed; this is called a deceleration
  • The sign therefore carries physical meaning, because a minus sign in front of an acceleration is the maths telling you the motion is slowing
Two examples of the sign of acceleration: a launching rocket labelled a = +30 m/s² speeding up, and a car being slowed by a person labelled a = −5 m/s² decelerating, showing positive acceleration means gaining speed and negative means losing speed
Source: Acceleration by Save My Exams
Worked example

Finding acceleration from a velocity–time graph

A straight line on a velocity–time graph passes through the point (6 m/s, t = 0) and rises to (30 m/s, t = 40 s).

Solution:

  • Change in velocity: 30 − 6 = 24 m/s
  • Time interval: 40 s
  • Acceleration = change in velocity ÷ time = 24 ÷ 40 = 0.6 m/s²