physics
posted by Kayla .
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?

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 = (90t1)
solve for t1, t2 then x2 etc
Respond to this Question
Similar Questions

physics
An ice sled powered by a rocket engine starts from rest on a large frozen lake and accelerates at +40 ft/s2. After some time t1, the rocket engine is shut down and the sled moves with constant velocity v for a time t2. If the total … 
physics
An ice sled powered by a rocket engine starts from rest on a large frozen lake and accelerates at +13.0 m/s^2. At t(subscript 1), the rocket engine is shut down and the sled moves with a constant velocity v until t(subscript 2). The … 
Physics
An ice sled powered by a rocket engine starts from rest on a large frozen lake and accelerates at +42 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 … 
Physics
An ice sled powered by a rocket engine starts from rest on a large frozen lake and accelerates at +13.0 m/s^2. At t1 the rocket shut down and the sled moves with constant velocity v until t2. The total distance traveled by the sled … 
Physics
An ice sled powered by a rocket engine starts from rest on a large frozen lake and accelerates at 15.0 m/s 2 . At t1 the rocket engine is shut down and the sled moves with constant velocity v for another t2 s. The total distance traveled … 
PHYSICS
A catapult launches a rocket at an angle of 56.9° above the horizontal with an initial speed of 100 m/s. The rocket engine immediately starts a burn, and for 3.25 s the rocket moves along its initial line of motion with an acceleration … 
Physics
A rocket of mass 1.0x10^3kg is being fired to a height of 5.0 x 10^3 m. The rocket engine shuts off when the rocket reaches a height of 1.0x10^3m, and the rocket coasts up to 5.0 x 10^3 m. A) What velocity must the rocket have at the … 
Physics
A model rocket launches with an initial velocity of 6 m/s, at an angle of 90 degrees (with respect to the horizon). The rocket's engine provides an acceleration of 2.2 m/s2, acting in the same direction as the initial velocity. After … 
physics
A test rocket is launched vertically from ground level (y = 0 m), at time t = 0.0 s. The rocket engine provides constant upward acceleration during the burn phase. At the instant of engine burnout, the rocket has risen to 49 m and … 
Physics
An ice sled powered by a rocket engine starts from rest on a large frozen lake and accelerates at +15.0 m/s2. At tl = 2.8 s the rocket engine is shut down and the sled moves with constant velocity v. At the 7800 m mark, the sled begins …