IGCSE Physics 0625

Topic: 1.2 Motion

Objective: Calculate speed from the gradient of a straight-line section of a distance-time graph

This section explains how to calculate the speed of an object when its motion is represented by a straight-line section on a distance-time graph. Understanding the relationship between distance, time, and speed is fundamental to kinematics.

Understanding Distance-Time Graphs

A distance-time graph plots the distance an object travels against the time taken. A straight line on this graph indicates that the object is moving at a constant speed. The slope of this line represents the speed.

Speed and Distance-Time Graphs

The speed of an object is defined as the distance it travels divided by the time taken. On a distance-time graph, the distance is represented on the y-axis and the time is represented on the x-axis. Therefore, the gradient of a straight-line section of a distance-time graph directly corresponds to the speed of the object.

Formula

Speed ($v$) = $\frac{\text{Distance (Δd)}}{\text{Time (Δt)}}$

On a distance-time graph, the distance is the change in distance (Δd) and the time is the change in time (Δt). So, the formula can be written as:

$v = \frac{\Delta d}{\Delta t} = \frac{d_2 - d_1}{t_2 - t_1}$

Steps to Calculate Speed

1. Identify a straight-line section on the distance-time graph. This indicates constant speed.
2. Determine the change in distance (Δd). This is the difference between the distance at the end of the straight-line section ($d_2$) and the distance at the beginning of the straight-line section ($d_1$).
3. Determine the change in time (Δt). This is the difference between the time at the end of the straight-line section ($t_2$) and the time at the beginning of the straight-line section ($t_1$).
4. Calculate the speed using the formula: $v = \frac{\Delta d}{\Delta t}$
5. Include appropriate units for speed. The standard unit for speed is meters per second (m/s).

Example

Consider a distance-time graph where a car travels a distance of 100 meters in 5 seconds along a straight line. What is the speed of the car?

Solution:

$d_1 = 0 \text{ m}$

$d_2 = 100 \text{ m}$

$t_1 = 0 \text{ s}$

$t_2 = 5 \text{ s}$

$\Delta d = d_2 - d_1 = 100 \text{ m} - 0 \text{ m} = 100 \text{ m}$

$\Delta t = t_2 - t_1 = 5 \text{ s} - 0 \text{ s} = 5 \text{ s}$

$v = \frac{\Delta d}{\Delta t} = \frac{100 \text{ m}}{5 \text{ s}} = 20 \text{ m/s}$

Therefore, the speed of the car is 20 m/s.

Table Summary

Concept	Description
Distance-Time Graph	Plots distance against time. A straight line indicates constant speed.
Speed	The rate at which an object covers distance.
Formula	$v = \frac{\Delta d}{\Delta t}$
Units of Speed	m/s (meters per second)