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Q.

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

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a

1.603 m/s2

b

2.603 m/s2

c

0.903 m/s2

d

0.603 m/s2

answer is D.

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Detailed Solution

a=4v or dvdt=4v ∴ ∫6vvdv=∫2t4dt ∴ v22-18=4t-8 v=8t+20 ∴  a=dvdt=48t+20   At   t=3 s, a=0.603 m/s2
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A particle travels in a straight line, such that for a short time 2 s≤t≤6 s, its motion is described by v=(4/a)m/s, where a is in m/s2. If v=6 m/s when t=2 s, determine the particle's acceleration when t=3 s.