Question

A car accelerates from rest at a constant rate of for some time; after which it decelerates at constant rate of β to come to rest. If the total time elapsed, is T second. (i) Draw a velocity time graph for the motion.

Answer 1

Answer:

$v = \frac{ \alpha \beta }{ \alpha + \beta } t$

Explanation:

Let maximum velocity=v

Now,v=0+αt1

Similarly, 0=v−βt2

From the above equations we get,

$t1 = \frac{v}{ \alpha }$

&

$t2 = \frac{v}{ \beta }$

$t1 + t2 = t = \frac{v}{ \alpha } + \frac{v}{ \beta }$

$= > v = \frac{ \alpha \beta }{ \alpha + \beta } t$

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