3. (20 pts) At the top of a hill, a small child takes a running start and hops on a sled at 5 m/s. Because
of the sloped hill and the small (but not negligible) friction, the acceleration of the sled while traveling
down the hill is 3 m/s2. Assume that this acceleration is constant during the child’s trip down the hill.
a) (5 pts) By how much does the velocity of the child change during the 10 s trip down the hill?
How much the velocity changes is the area under the vvs. tplot. Since acceleration is constant here,
this is a rectangle with area at. Thus,
∆v=at = (3)(10) = 30 m/s
b) (5 pts) What is the final velocity of the child upon reaching the bottom of the hill, 10 s after hopping
on the sled?
The final velocity is the initial plus the amount of change. So we have
vf=vi+at = 5 + 30 = 35 m/s
c) (10 pts) How far did the child travel, while on the sled, to the bottom of the hill?
You could use
xf=xi+vit+1
2at2= (5)(10) + 1
2(3) (10)2= 200 m