A particle travels in a straight line such that for a short time 2s

Question

A particle travels in a straight line such that for a short time 2s < t < 6s, its motion is described by v=(4/a)m/s, where 'a' is in m/s 2 . If v=6m/s when t=2sec, determine the particle's acceleration when t=3 sec.

Badiuddin askIITians.ismu Expert · Answer

Dear Chilukuri

V=4/a

Va =4

V dv/dt =4

intigrate

V²/2 =4t +c1

V² =8t +c

apply given condition

36 =16 +c

c= 20

so

V² =8t +20

velocity at t=3 sec

V = √44

so acceleration a=4/v =4/√44

=2/√11 m/sec2

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LISA · Answer

From the given data: v=4/ams−1 Acceleration From on=? At time t=3s Given velocity is v=4/a⟹a=4/v⟹dv/dt=4/v.......(1) Let us integrate on both the side ∫vdv=∫4dt⟹v²/2−18=4t−8 v²/2=4t−8+18⟹v²=8t+20⟹v=√8t+20 Equation 1 implies a=dv/dt⟹a=√8t+20 The acceleration of the particle at time t = 3s a=4/√8(3)+20⟹a=0.603ms−²

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A particle travels in a straight line such that for a short time 2s t 6s, its motion is described by v=(4/a)m/s, where 'a' is in m/s 2 . If v=6m/s when t=2sec, determine the particle's acceleration when t=3 sec.

A particle travels in a straight line such that for a short time 2s<t<6s, its motion is described by v=(4/a)m/s, where 'a' is in m/s². If v=6m/s when t=2sec, determine the particle's acceleration when t=3 sec.

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