Question

The velocity-time graph of a track cyclist during a race is shown below. Work out the total distance travelled by the cyclist over the course of the race.

• A. $600m$
• B. $612.5m$
• C. $800m$
• D. $812.5m$

Answer 1

The correct option is D $812.5m$


The area under the velocity-time graph gives displacement.
Since, the velocity here is always positive, the area under this graph will give distance (i.e., distance = displacement).
Area covered from $t=0stot=10s\left(portionA\right)$ $=\frac{1}{2}\times 10\times 15=75$

Area covered from $t=10stot=15s\left(portionB\right)=$ $5\times \left(10\right)+\frac{1}{2}\times \left(5\right)\times \left(5\right)=62.5m$
Area covered from $t=15stot=20s\left(portionC\right)$
$=\left(5\right)\times \left(10\right)+\frac{1}{2}\times \left(10\right)\times \left(5\right)=75m$
Area covered from $t=20stot=50s\left(portionD\right)$
$=\left(30\right)\times \left(20\right)=600m$
Total distance covered $=75+62.5+75+600=812.5m$