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20 September, 19:14

A particle is moving along the x-axis so that its position at t ≥ 0 is given by s (t) = (t) In (5t). Find the acceleration of the particle when the velocity is first zero.

5e

5e2

e

None of these

+1
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  1. 20 September, 21:20
    0
    position = s (t) = (t) In (5t)

    velocity = ds/dt = t d/dt (ln (5t)) + d/dt (t) ln (5t)

    = t * 5 1/5t + ln (5t)

    = 1 + ln (5t)

    acceleration = dv/dt = d^2s/dt^2 = d/dt (1 + ln (5t))

    =d/dt (1) + d/dt (ln 5t)

    = 0 + 1/5t * 5

    = 1/t

    0 = 1 + ln (5t)

    -1 = ln (5t)

    e^-1 = 5t

    1/e = 5t

    1 / (5e) = t

    acceleration = 1/t = 1 / (1/5e) = 5e

    Answer: 5e
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