A particle travels in a straight line such that for a short time 2s2. If v=6m/s when t=2sec, determine the particle's acceleration when t=3 sec.

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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/s². If v=6m/s when t=2sec, determine the particle's acceleration when t=3 sec.

Chilukuri Sai Kartik , 16 Years ago

Grade 12

2 Answers

Badiuddin askIITians.ismu Expert

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

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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Last Activity: 16 Years ago

LISA

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

Last Activity: 4 Years ago

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Mechanics> Motion in 1 dimension...

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.

Chilukuri Sai Kartik , 16 Years ago

Badiuddin askIITians.ismu Expert

LISA

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