First slide

Rectilinear Motion

Question

An object, moving with a speed of 6.25 m/s, is declerated at a rate given by, $\frac{dv}{dt} = - 2 .5 \sqrt{v}$ where v is the instantaneous speed. The time taken by the
object, to come to rest would be

Moderate

A

2 s
B

4 s
C

8 s
D

1 s

Solution

Given ; $\frac{dv}{dt} = 2 .5 \sqrt{v}$
$\Rightarrow \frac{dv}{\sqrt{v}} = - 2 .5 dt$
$\Rightarrow \int_{6 .26}^{0} v^{- 1 / 2} dv = - 2 .5 \int_{0}^{t} dt$
$\Rightarrow - 2 .5 [t]_{0}^{t} = {[2 v^{1 / 2}]}_{6 .25}^{0}$
t = 2 s

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