The acceleration of a cart started at t=0,

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 $=t$

$5=\frac{v}{10}$

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

Distance=Area of $v$-t graph

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

$=1000 \mathrm{ft}$

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