# Solve the following :

Question:

The acceleration of a cart started at $t=0$, varies with time as shown in the given figure. Find the distance travelled in 30 seconds and draw the position-time graph.

Solution:

By velocity-time graph,

Acceleration $=$ slope $=t$

$\mathrm{V}=50 \mathrm{~m} / \mathrm{s}$.

Distance=Area of v-t graph

$=\frac{1}{2}(30+10)(50)$

$=\frac{1}{2}(30+10)(50)$

$=1000 \mathrm{ft}$