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# Speed-time graphs

A speed-time graph shows the time on the x-axis and speed on the y-axis.

The gradient of the graph gives the acceleration.

• A horizontal line indicates that the object is moving at a constant velocity.
• A positive gradient indicates that the object is accelerating.
• A negative gradient indicates that the object is decelerating.
• A curved line indicates non-uniform acceleration.

The area under the graph indicates the distance travelled.

To work out the distance travelled during $\Tblue{\text{section A}}$ on the graph we need to find the area of the triangle underneath the graph. $$\Tblue{\text{distance}} = \frac{1}{2} \times 10 \us \times 20 \umps = 100 \um$$

The distance travelled during $\Tred{\text{section B}}$ is equal to the area of the rectangle under the graph. $$\Tred{\text{distance}} = 10 \us \times 20 \umps = 200 \um$$

The total distance travelled is equal to the sum of the three sections $$\text{total distance} = 100 \um + 200 \um + 200 \um = 500 \um.$$