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Question

Velocity of the particle in a rectilinear motion is given as v=3t45t in m/s. Find
(i) Acceleration at 2 sec.
(ii) Average acceleration in 2 sec.

A
(i) 71 m/s2
(ii) 17 m/s2
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B
(i) 81 m/s2
(ii) 18 m/s2
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C
(i) 91 m/s2
(ii) 19 m/s2
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D
(i) 61 m/s2
(ii) 16 m/s2
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Solution

The correct option is C (i) 91 m/s2
(ii) 19 m/s2
Given, v=3t45t
(i) Acceleration at 2 sec means we have to find out the instantaneous acceleration at 2 sec
a(t)=dv(t)dt=d(3t45t)dt=12t35
a|@t=2 sec=12×235=91 m/s2

(ii) Average acceleration in 2 sec is given by
¯a=(vfvi)Δt
vf|@t=2 sec=3×245×2=38 m/s
vi|@t=0 sec=3×045×0=0 m/s
¯a=(vfvi)Δt=3802=19 m/s2

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