# Speed-time and velocity-time graphs - Higher

Speed-time graphs show speed on the vertical axis and time on the horizontal axis. The gradient of a speed-time graph represents acceleration because:

= metres per second per second.

Metres per second per second can be written as or .

A negative gradient shows the rate of 'slowing down' or deceleration.

Velocity-time graphs show velocity on the vertical axis. Acceleration is still represented by the gradient.

The gradient of speed-time and velocity-time graphs represent acceleration.

The area under a speed-time graph represents the distance travelled. Likewise, the area under a velocity-time graph represents the of the moving object. If the velocity is always positive, then the displacement will be the same as the distance.

### Example

Describe what is happening in this journey.

Between 0 and 4 seconds:

• the object is accelerating at
• it travels

Between 4 and 7 seconds:

• the object is travelling at a constant velocity of 8 m/s
• it travels

Between 7 and 10 seconds:

• the object is accelerating at
• this means it is slowing down or decelerating at a rate of
• it travels