an ice sled powered by rocket engine starts from rest om a large frozen lake and accelerates at +13.0 m/s/s.
at t1 the rocket engine is shut down and the sled moves with conestant velocity V until t2.
the total distance traveld by the seld is 5.30x(10 to the power 3) m and the total time is 90.0s.find t1, t2 and v

If you can sketch the velocity-time graph for the motion of this ice sled, you will get all the answers easily.

The total distance travelled is given by the area under the velocity-time graph, that is the area of a trapezium with parallel sides t_2 - t_1 and t_2 and a perpendicular height equal to the final velocity v.

Since the total time is t2, that means t2 = 90.0 s.

The equation for the velocity at time t1 is given by:

Velocity at time t1 = 0.5a(t1)^2

Since the acceleration is 13, you can find v in terms of t1.

Then replace v in the total distance equation to find the time t1.

After that, you can easily use the time t1 to find the value of v.

Post what you get! :)

And lastly, this problem has nothing to do with free fall... =/

I was about to answer this one but I had to go to class! I get back and boom it's done.

Well lets see what I did.

It gives you total time and total distance.

From this I got an average velocity. I then plugged it into the kinematic equation: Vf=Vi+at and solved for t.

This gives you the time it took to accelerate, or T1.

T2 is 90s

Distance at T2 is 3500

Find the distance at T1: Xt1=.5a(t1^2)

v=(Xt2-Xt1)/(T2-T1)

That's my version!