Calculating Acceleration from Speed-Time Graphs (Cambridge (CIE) IGCSE Physics): Revision Note

Interpreting speed-time graphs

Extended tier only

• When interpreting speed-time graphs, the shape of the graph can show:

  • constant acceleration

  • changing acceleration

• The gradient of a speed-time graph shows the acceleration of a moving object

  • The gradient is positive if the object is accelerating (speed increases with time)

  • The gradient is negative if the object is decelerating (speed decreases with time)

Interpreting constant positive acceleration on a speed-time graph

• When the acceleration is constant and non-zero:

  • the graph is a straight line

  • velocity is increasing at a constant rate, i.e. speed changes by the same amount in equal intervals of time

Constant positive acceleration on a speed-time graph

Interpreting increasing positive acceleration on a speed-time graph

• When the acceleration is increasing:

  • the graph is a curve 

  • velocity is increasing at an increasing rate, i.e. the speed changes by the same amount in increasingly shorter time intervals

Increasing positive acceleration on a speed-time graph

Interpreting decreasing positive acceleration on a speed-time graph

• When the acceleration is decreasing:

  • the graph is a curve

  • velocity is increasing at a decreasing rate, i.e. the speed changes by the same amount in increasingly longer time intervals

Decreasing positive acceleration on a speed-time graph

Interpreting decreasing negative acceleration on a speed-time graph

• When the deceleration is decreasing:

  • the graph is a curve

  • the velocity is decreasing at a decreasing rate, i.e. the speed changes by the same amount in increasingly longer intervals of time

Decreasing negative acceleration on a speed-time graph

Calculating acceleration

Extended Tier Only

• The acceleration of an object (opens in a new tab) can be calculated from the gradient of a speed-time graph

Finding the gradient when acceleration is constant

• When acceleration is constant, the speed-time graph will be a straight line

• The gradient of a straight line can be found using:

 $\mathrm{gradient}=\frac{∆y}{∆x}$

• Where:

  • $∆y$ = change in $y$ (speed) values

  • $∆x$ = change in $x$ (time) values

• Therefore, the gradient is equal to:

$a=\frac{∆v}{∆t}$

• Where:

  • $a$ = acceleration, measured in metres per second squared (m/s²)

  • $∆v$ = change in speed, measured in metres per second (m/s)

  • $∆t$ = change in time, measured in seconds (s)

Finding the gradient when acceleration is changing

• When acceleration is changing, the speed-time graph will be a curve

• The gradient of a point on a curve can be found by drawing a tangent to the curve

  • A tangent to the curve is a straight line drawn to match the gradient of the curve at a specific point

A tangent to the curve

• The tangent provides a gradient that is representative of the gradient at a specific point on the curve

• The gradient of the tangent can be found using:

$\mathrm{gradient}=\frac{∆y}{∆x}$

• The value of the gradient at a specific point on the curve represents the acceleration of the object at that moment

  • This is called instantaneous acceleration