Page:Calculus Made Easy.pdf/84

When ${\displaystyle t=2.11}$,

When ${\displaystyle t=3.03}$,

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

Exercises V (See page 256 for Answers)

(1) If ${\displaystyle y=a+bt^{2}+ct^{4}}$; find ${\displaystyle {\dfrac {dy}{dt}}}$ and ${\displaystyle {\dfrac {d^{2}y}{dt^{2}}}}$.

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

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

(4) If a body move according to the law

find its velocity when ${\displaystyle t=4}$ seconds; ${\displaystyle s}$ being in feet.