Physics

Problem

During the interval

-\tau \le t \le \tau

a force

F(t)=A t^{3}-B t

acts on a body of mass

m

moving along a straight line. Outside this interval the force is zero. a. (i) Show that the total impulse delivered in the full interval

-\tau

\tau

is zero if and only if

A\tau^{4}=B\tau^{2}

. b. (ii) Hence obtain the required relation between

A

and

B

. c. (iii) If

\tau=0.50\,\text{s}

and

B=80\,\text{N s}^{-1}

, calculate

A

. d. (iv) Suppose instead that

A=400\,\text{N s}^{-3}

and

B

satisfies the condition from part (ii). The body enters the interval with velocity

-3.0\,\text{m s}^{-1}

(negative sign indicates motion opposite to the force for

t>0

). Determine its velocity on leaving the interval at

t=\tau