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Introduction to Equations of Motion

A car acceler...

Question

A car accelerates from rest with $2 m s^{- 2}$ for $2 s$ and then decelerates constantly with $4 m s^{- 2}$ for $t_{0}$ second to come to rest. The graph for the motion is shown in fig.
Find the maximum speed attained by the car.

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Solution

Maximum speed of the car will be at $t = 2 s$ ,because area is positive till that time.
Change in velocity = Area of $a - t$ graph
$\Rightarrow v_{m a x} - 0 = 2 \times 2 \Rightarrow v_{m a x} = 4 m s^{- 1}$

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