JEE Main · 2012 · 29 Apr 2012 · Offline · Laws of Motion

A particle of mass

m

is at rest at the origin at time

t = 0

. It is subjected to a force

F (t) = F_{0} e^{- b t}

in the

x

direction. Its speed

v (t)

is depicted by which of the following curves?

(A)(see structure)
(B)(see structure)
(C)(see structure)
✓ Correct

Answer: (C)

Solution

The force

F = F_{0} e^{- b t}

gives an acceleration

a = \frac{F _{0}}{m} e^{- b t}

. Since the particle starts from rest, integrate from time zero:

v = \int_{0}^{t} \frac{F _{0}}{m} e^{- b t^{'}} d t^{'} = \frac{F _{0}}{mb} (1 - e^{- b t})

. At

t = 0

this is zero, and as time grows the speed rises steadily and approaches the limiting value

\frac{F _{0}}{mb}

. The speed therefore starts at zero and bends over to flatten against a horizontal asymptote.

JEE Main · 2012 · 29 Apr 2012 · Offline · Single correct option

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