A particle starts with an initial velocity of $10.0 \mathrm{~ms}^{-1}$ along x-direction and accelerates uniformly at the rate of $2.0 \mathrm{~ms}^{-2}$. The time taken by the particle to reach the velocity of $60.0 \mathrm{~ms}^{-1}$ is ______.

JEE Main · 2023 · 06 Apr 2023 · Shift 2 · Kinematics

A particle starts with an initial velocity of

10.0 ms^{- 1}

along x-direction and accelerates uniformly at the rate of

2.0 ms^{- 2}

. The time taken by the particle to reach the velocity of

60.0 ms^{- 1}

is ______.

(A)6 s
(B)3 s
(C)30 s
(D)25 s✓ Correct

Answer: (D)

Solution

The motion is uniformly accelerated, so

v = u + a t

with

u = 10.0

m s

^{- 1}

a = 2.0

m s

^{- 2}

and

v = 60.0

m s

^{- 1}

. Then

t = \frac{v - u}{a} = \frac{60.0 - 10.0}{2.0}

. The time taken to reach the given velocity is

25

JEE Main · 2023 · 06 Apr 2023 · Shift 2 · Single correct option

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