Calculate acceleration from the gradient of a speed-time graph

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IGCSE Physics - 1.2 Motion - Acceleration from Speed-Time Graphs

IGCSE Physics - 1.2 Motion

Calculating Acceleration from a Speed-Time Graph

This section explains how to calculate acceleration using a speed-time graph. Acceleration is the rate of change of velocity. A speed-time graph plots the speed of an object against time.

Understanding Speed-Time Graphs

A speed-time graph is a simple graph where the y-axis represents the speed (or velocity, if direction is considered) of an object and the x-axis represents time.

Suggested diagram: A speed-time graph showing a straight line with a positive gradient representing constant acceleration.

The gradient of a speed-time graph represents the acceleration of the object. A positive gradient indicates acceleration, a negative gradient indicates deceleration (or retardation), and a zero gradient indicates constant speed.

Calculating Acceleration

Acceleration is calculated as the change in velocity divided by the time interval over which the change occurs.

In a speed-time graph, the change in velocity is the difference between the final speed and the initial speed. The time interval is the difference between the final time and the initial time.

Therefore, the formula for acceleration (a) is:

$$a = \frac{\text{Change in speed}}{\text{Time interval}} = \frac{\text{Final speed} - \text{Initial speed}}{\text{Final time} - \text{Initial time}}$$

Steps to Calculate Acceleration from a Speed-Time Graph

  1. Identify the initial speed (u) and the final speed (v) from the graph. Look at the y-axis to find these values.
  2. Identify the initial time (ti) and the final time (tf) from the graph. Look at the x-axis to find these values.
  3. Calculate the change in speed (v - u).
  4. Calculate the time interval (tf - ti).
  5. Calculate the acceleration using the formula: a = (v - u) / (tf - ti).
  6. State the acceleration with the correct units (e.g., m/s2).

Example Calculation

Consider a speed-time graph where:

  • Initial speed (u) = 2 m/s
  • Final speed (v) = 8 m/s
  • Initial time (ti) = 1 s
  • Final time (tf) = 5 s

Using the formula:

$$a = \frac{8 \text{ m/s} - 2 \text{ m/s}}{5 \text{ s} - 1 \text{ s}} = \frac{6 \text{ m/s}}{4 \text{ s}} = 1.5 \text{ m/s}^2$$

Therefore, the acceleration is 1.5 m/s2.

Table Summary

Quantity Symbol Units
Initial Speed u m/s
Final Speed v m/s
Initial Time ti s
Final Time tf s
Acceleration a m/s2