Figure $1$: Problem $1$b

Total points $=25$ points

Instructions: Write your answers in the space provided.

Q$1$: $($a$)$ A mechanic pushes a $2\mathrm{.}50\backslash$times $10^(3)$Kg car from rest to a speed of v$,$

doing $5\mathrm{.}00\backslash$times $10^(3)$J of work in the process. During this time, the

car moves $25\mathrm{.}0$ m $.$ Neglecting friction between car and road, find

i$.$ The velocity v$,$ and

ii$.$ The horizontal force exerted on the car

$($b$)$ A ball of mass m$=1\mathrm{.}80$Kg is released from rest at a height

h$=65\mathrm{.}0$cm above a light vertical spring of force constant k as

in the figure $1-$a$.$ The ball strikes the top of the spring and

compresses it a distance d$=9\mathrm{.}00$cm as in figure $1-$b$.$ Neglecting

any energy losses during the collision, find:

i$.$ The speed of the ball as it touches the spring, and

ii$.$ the force constant of the spring