A car of mass $1000 \mathrm{~kg}$ is moving at a speed of 30 $\mathrm{m} / \mathrm{s}$. Brakes are applied…

A car of mass $1000 \mathrm{~kg}$ is moving at a speed of 30 $\mathrm{m} / \mathrm{s}$. Brakes are applied to bring the car to rest. If the net retarding force is $5000 \mathrm{~N}$, the car comes to stop after travelling $d \mathrm{~m}$ in $t \mathrm{~s}$. Then
  1. $d=150, t=5$
  2. $d=120, t=8$
  3. $d=180, t=6$
  4. $d=90, t=6$

Solution

Given: mass of car $m=1000 \mathrm{~kg}$ $ \begin{aligned} & u=30 \mathrm{~m} / \mathrm{s} \\ & v=0 \mathrm{~m} / \mathrm{s} \\ & \text { retarding force } f=5000 \mathrm{~N} \\ & \therefore \text { retardation, }-a=\frac{5000}{1000}=5 \mathrm{~m} / \mathrm{s}^2 \end{aligned} $ By equation, $v^2-u^2=2$ as $ \begin{aligned} & 0-(30)^2=-2 \times 5 \times d \\ & \therefore d=\frac{900}{10}=90 \mathrm{~m} \end{aligned} $ and $a=\frac{v-u}{t} \therefore t=\frac{v-u}{a}=\frac{0-30}{-5}=6 \mathrm{~s}$

Asked in: JEE Main 2012 (07 May Online)

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