Kinematics

JEE Main level, numerical answer, medium

51 of 308

Question 51 of 308

A car is moving with speed of 150kmh−1150km{h}^{-1} and after applying the brake it will move 27m27m before it stops. If the same car is moving with a speed of one third the reported speed then it will stop after travelling _____ mm distance.

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Answer: 3

In both cases, the final velocity is zero. Using equation of motion for constant acceleration
v2=u2+2as{v}^{2}={u}^{2}+2as
⇒02−u2=−2a(27)...(1)\Rightarrow {0}^{2}-{u}^{2}=-2a\left(27\right)...\left(1\right)
⇒02−(u3)2=−2as′...(2)\Rightarrow {0}^{2}-{\left(\dfrac{u}{3}\right)}^{2}=-2a{s}^{'}...\left(2\right)
From (1)\left(1\right) and (2)\left(2\right),
2a(27)=9(2as′)2a\left(27\right)=9\left(2a{s}^{'}\right)
⇒s′=3m\Rightarrow {s}^{'}=3m

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