Question

An ice sled powered by a rocket engine starts from rest on a large frozen lake and accelerates at +35 ft/s2. After some time t1, the rocket engine is shut down and the sled moves with constant velocity v for a time t2. Assume the total distance traveled by the sled is 16350 ft and the total time is 90 s.

(a) Find the times t1 and t2.
(b) Find the velocity v.

At the 16350 ft mark, the sled begins to accelerate at -22 ft/s2.
(c) What is the final position of the sled when it comes to rest?
(d) What is the duration of the entire trip?

Answer 1

Start at xo
While accelerating
v = 35 t
d = 0 + 0t + (35/2) t^2
at x1,t1
v1 = 35 t1
x1 = 17.5 t1^2
------------------------
While coasting
v2=v1= 35 t1 + 0
d = 17.5 t1^2 + (35 t1)t + (1/2)0
at x2,t2
x2 = 17.5t1^2 + 35 t1(t2)
so
17.5 t1^2 + 35 t1 t2 =16350
t1+t2 = 90 so t2 = (90-t1)
solve for t1, t2 then x2 etc