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Question

A particle is moving in a straight line so that after t seconds its distance is s( in cms) from a fixed point on the line is given by s=f(t)=8t+t3.Find:
1.the velocity at time t=2sec
2.the initial velocity
3.acceleration at t=2sec

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Solution

Given displacement of the particle is s=f(t)=8t+t3 cm
Velocity of particle at time t is v=f(t)=8+3t2 cm/sec
1)Velocity of particle at time t=2 sec is v=8+3(2)3=32 cm/sec
2)Initial velocity is v=8+3(0)3=8 cm/sec
Acceleration of particle at time t is dvdt=6t cm/s2
3)Acceleration at t=2 sec is a=6(2)=12 cm/s2

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