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
$=\frac{1}{2}(30+10)(50)$
$=\frac{1}{2}(30+10)(50)$
$=1000 \mathrm{ft}$
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