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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 i) the velocity at time t = 2 sec ii) the initial velocity iii) acceleration at t = 2 sec. |
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Answer» Given S = f(t) = 8t + t3 i) ds/dt = 8 + 3t2 (ds/dt)t = 2 = 8 + 3(2)2 = 8 + 12 = 20 ∴ The velocity at time t = 2 is 20 cm / sec ii) (ds/dt)t = 0 = 8 + 0 = 8 ∴ Initial velocity = 8cm / sec iii) d2s/dt2 = 0 + 6t (d2s/dt2)t= 2 = 6(2) = 12 cm / sec2 Acceleration at t = 2 is 12 cm / sec2 |
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