Question

# Velocity of the particle in a rectilinear motion is given as v=3t4−5t 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/s2Given, v=3t4−5t (i) Acceleration at 2 sec means we have to find out the instantaneous acceleration at 2 sec ⇒ a(t)=dv(t)dt=d(3t4−5t)dt=12t3−5 ⇒ a|@t=2 sec=12×23−5=91 m/s2 (ii) Average acceleration in 2 sec is given by ¯a=(vf−vi)Δt vf|@t=2 sec=3×24−5×2=38 m/s vi|@t=0 sec=3×04−5×0=0 m/s ¯a=(vf−vi)Δt=38−02=19 m/s2

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