At time t, the velocity v(t) of an object moving in a straight line satisfies
(a) Show that , where v0 denotes the velocity of the object at time t = 0 (and we assume v0 > 0). Hence prove that the object comes to rest after a finite time tan−1(v0). Does the object remain at rest?
(b) Use the chain rule to show that (1.4.17) can be written as where x(t) denotes the distance traveled by the object at time t , from its position at t = 0. Determine the distance traveled by the object when it first comes to rest.
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