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The acceleration of a particle is increasing linearly with time t as bt. The particle starts from the origin with an initial velocity v0. The distance travelled by the particle in time t will be (a) v0t + 1/3 bt2 (b) v0t + 1/3 bt3 (c) v0t + 1/2 bt3 (d) v0t + 1/2 bt2

The acceleration of a particle is increasing linearly with time t as bt. The particle starts from the origin with an initial velocity v0. The distance travelled by the particle in time t will be
    (a)    v0t + 1/3 bt2
    (b)    v0t + 1/3 bt3
    (c)    v0t + 1/2 bt3
    (d)    v0t + 1/2 bt2

Grade:upto college level

1 Answers

Radhika Batra
247 Points
8 years ago

(c)

    dv/dt = bt; Integrated ∫¦dv=∫¦?bt dt?

    v = (bt^2)/2 + c        [t = 0, v = v0]

    v = v0 + (bt^2)/2

    s = v.t = v0t + (bt^3)/2

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