    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 option is D Velocity of particle is zero at t=2√3+2 secGiven v=p+qt+rt2 at t=0,v=4 ⇒4=p+0+0⇒p=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×2⇒r=−12 =−0.5 ∴v=4+2t−12t2 Velocity at t=2 v(2)=4+2×2+(−12)×22=6 m/s If velocity is zero, v=0=8+4t−t2(t−2)2=12t=2√3+2 sec  Suggest Corrections  0      Similar questions  Related Videos   Speed and Velocity
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