• The slope on a distance-time graph represents the speed of an object.
• The velocity of an object is its speed in a particular direction.
• The slope on a velocity-time graph represents the acceleration of an object.
• The distance travelled is equal to the area under a velocity-time graph.

Speed, Distance and Time

speed (metres per second, m/s) = distance travelled (metre, m) ÷ time taken (second, s)

distance (metre, m) = speed (metres per second, m/s) x time (seconds, s)

time (second, s) = distance (metre, m)  ÷ speed (metres per second, m/s)

Distance-time graph

Background information

You should be able to draw and explain distance-time graphs for objects moving at steady speeds or standing still.

The vertical axis of a distance-time graph is the distance travelled from the start. The horizontal axis is the time from the start.

When an object is stationary, the line on the graph is horizontal. When an object is moving at a steady speed, the line on the graph is straight, but sloped.

Note:

the steeper the line, the greater the speed of the object. 

Velocity time-graphs

You should be able to explain velocity-time graphs for objects moving with a constant velocity or constant acceleration.

The velocity of an object is its speed in a particular direction. This means that two cars travelling at the same speed, but in opposite directions, have different velocities.

The vertical axis of a velocity-time graph is the velocity of the object. The horizontal axis is the time from the start.

When an object is moving with a constant velocity, the line on the graph is horizontal. When an object is moving with a constant acceleration, the line on the graph is straight, but sloped.

The steeper the line, the greater the acceleration of the object.

A line sloping downwards - with a negative gradient - represents an object with a constant deceleration - slowing down.

Acceleration

You should be able to calculate the acceleration of an object from its change in velocity and the time taken.

The equation

When an object moves in a straight line with a constant acceleration, you can calculate its acceleration if you know how much its velocity changes and how long this takes. This equation shows the relationship between acceleration, change in velocity and time taken.

acceleration (meters per second squared) = change in velocity (m/s)  ÷ time taken (second)

Distance-time graphs - higher

You should be able to calculate gradients on distance-time graphs.

To calculate the gradient of the line on a graph, divide the change in the vertical axis by the change in the horizontal axis.

The gradient of a line on a distance-time graph represents the speed of the object.

Velocity-time graphs - higher

You should be able to calculate gradients of velocity-time graphs and the areas under the graphs.

The gradient of a line on a velocity-time graph represents the acceleration of the object. Study this velocity-time graph.

The area under the line in a velocity-time graph represents the distance travelled. 

Key: Light Blue- w = 4 h = 8          Dark Blue- w = 6 h = 8

1. Area of light-blue triangle
   • The width of the triangle is 4 seconds and the height is 8 metres per second. To find the area, you use the equation:
   • area of triangle = ¹⁄₂ × base × height
   • so the area of the light-blue triangle is ¹⁄₂ × 8 × 4 = 16m.
2. Area of dark-blue rectangle
   • The width of the rectangle is 6 seconds and the height is 8 metres per second. So the area is 8 × 6 = 48m.
3. Area under the whole graph
   • The area of the light-blue triangle plus the area of the dark-blue rectangle is:
   • 16 + 48 = 64m.
   • This is the total area under the distance-time graph. This area represents the distance covered.

Summary:

the gradient of a velocity-time graph represents the acceleration

the area under a velocity-time graph represents the distance covered