Laws of Motion

JEE Main level, single correct, medium

58 of 210

Question 58 of 210

A car of mass 1000 kg1000 \mathrm{~kg} is moving at a speed of 30 m/s\mathrm{m} / \mathrm{s}. Brakes are applied to bring the car to rest. If the net retarding force is 5000 N5000 \mathrm{~N}, the car comes to stop after travelling d md \mathrm{~m} in t st \mathrm{~s}. Then

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Answer: (D) d=90,t=6d=90, t=6

Given: mass of car m=1000 kgm=1000 \mathrm{~kg}
u=30 m/sv=0 m/s retarding force f=5000 N∴ retardation, −a=50001000=5 m/s2\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, v2−u2=2v^2-u^2=2 as
0−(30)2=−2×5×d∴d=90010=90 m\begin{aligned} & 0-(30)^2=-2 \times 5 \times d \\ & \therefore d=\frac{900}{10}=90 \mathrm{~m} \end{aligned}
and a=v−ut∴t=v−ua=0−30−5=6 sa=\frac{v-u}{t} \therefore t=\frac{v-u}{a}=\frac{0-30}{-5}=6 \mathrm{~s}

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