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Question

Velocity of a particle as a function of time is shown in graph which is a parabola. If slope of the graph at t=0 is 2 units and v=p+qt+rt2, then (Assume SI units everywhere)

A
q=4
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B
r=0.5
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C
v0=6 m/s
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D
Velocity of particle is zero at t=23+2 sec
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Solution

The correct options are
B r=0.5
C v0=6 m/s
D Velocity of particle is zero at t=23+2 sec
Given v=p+qt+rt2
at t=0,v=4 4=p+0+0p=4 -- (1)
a=dvdt=q+2rt
at t=0, slope =a=2
2=q+0 and q=2 -- (2)
From graph, slope = 0 at t = 2
0=2+2r×2r=12 =0.5
v=4+2t12t2
Velocity at t=2
v(2)=4+2×2+(12)×22=6 m/s
If velocity is zero,
v=0=8+4tt2(t2)2=12t=23+2 sec

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