JEE Main · 2017 · 02 Apr 2017 · Offline · Work, Power & Energy

A time dependent force

F = 6 t

acts on a particle of mass 1 kg . If the particle starts from rest, the work done by the force during the first 1 sec . will be :

(A)9 J
(B)18 J
(C)4.5 J✓ Correct
(D)22 J

Answer: (C)

Solution

With

F = 6 t

on a

1

kg mass the acceleration is

6 t

, so the speed builds as

v = \int_{0}^{t} 6 t d t = 3 t^{2}

, reaching

3

m/s at

t = 1

s. By the work-energy theorem the work done equals the kinetic energy gained,

\frac{1}{2} (1) (3)^{2} = 4.5

JEE Main · 2017 · 02 Apr 2017 · Offline · Single correct option

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