At time t, the velocity v(t) of an object moving in a straight line satisfies dv dt = (1

Chapter 1, Problem 21

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At time t, the velocity v(t) of an object moving in a straight line satisfies dv dt = (1 + v2). (1.4.22) (a) Show that tan1(v) = tan1(v0) t, 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 tan1(v0). Does the object remain at rest? (b) Use the chain rule to show that (1.4.22) can be written as v dv dx = (1+v2), where x(t) denotes the distance travelled by the object at time t, from its position at t = 0. Determine the distance travelled by the object when it first comes to rest.