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Question

A particle moves in a circle of radius 1.0 cm at a speed given be v=2.0t where v is in cm/s and t is in seconds. Find the magnitude of net acceleration at t=1 s.

A
4 cm/s2
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B
2 cm/s2
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C
20 cm/s2
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D
10 cm/s2
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Solution

The correct option is C 20 cm/s2
Given,
v=2.0t
r=1.0 cm
As we know,
a) Radial acceleration (ar)=v2r
(Radial acceleration does not depends upon the instantaneous velocity and will be constant throughout the motion because radial acceleration is perpendicular to the tangential velocity)
Velocity v (t=1 s) = 2×1=2 cm/s
hence, radial acceleration (ar)=v2r=221=4 cm/s2

b) Tangential acceleration (at)
(tangential acceleration will be in the direction of the instantaneous velocity)
v=2 t
Differentiate both side w.r.t. time, hence
dvdt=2
Tangential acceleration at=dvdt=2 cm/s2

Magnitude of net acceleration (aT) aT=(a2r)+(at)2
aT=(4)2+(2)2
aT=20 cm/s2

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