Page:Calculus Made Easy.pdf/84

 When $$t=2.11$$,

When $$t=3.03$$,

The velocity is reversed. The wheel is evidently at rest between these two instants; it is at rest when $$\omega = 0$$, that is when $$0=2-0.3t^3$$, or when $$t=2.58$$ sec., it has performed

Exercises V (See page 256 for Answers) (1) If $$y = a + bt^2 + ct^4$$; find $$\dfrac{dy}{dt}$$ and $$\dfrac{d^2y}{dt^2}$$.

(2) A body falling freely in space describes in $$t$$ seconds a space $$s$$, in feet, expressed by the equation $$s=16t^2$$. Draw a curve showing the relation between $$s$$ and $$t$$. Also determine the velocity of the body at the following times from its being let drop: $$t=2$$ seconds; $$t=4.6$$ seconds; $$t=0.01$$ second.

(3) If $$x=at-\tfrac{1}{2}gt^2$$; find $$\dot{x}$$ and $$\ddot{x}$$.

(4) If a body move according to the law

find its velocity when $$t=4$$ seconds; $$s$$ being in feet.