Radial & Tangential Acceleration for Non Uniform Circular Motion
A particle mo...
Question
A particle moves in a circle of radius 4m at a speed given by v=4t, where v is in m/s and t in seconds. The total acceleration of particle at t=1s is :
A
4 m/s2
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B
4√3 m/s2
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C
8 m/s2
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D
4√2 m/s2
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Solution
The correct option is D 4√2 m/s2 Given that particle is moving in circular path of radius (r=4m) with speed, v=4t. It means that it is a case of non-uniform circular motion.
∴The acceleration of particle will contain tangential acceleration at as well as centripetal acceleration, ac.
We know that acceleration is the rate of change of velocity per unit of time.
∴at=dvdtat=ddt(4t)=4m/s2
at t=1s,v=4m/s, hence centripetal acceleration, ac=v2r∴ac=424=4m/s2 ⇒Total acceleration aT of particle given by: aT=√at2+ac2∴aT=√42+42=4√2m/s2