Kinematics problem, is it possible to solve with given information?

Well, the first part of the question asks you to find the acceleration before the rocket has the constant acceleration, therefore having the constant velocity. To answer the question for the first part, we need to break into parts.. We know that:

→v_0 = 0 m/s
→t = 20 s
→d = 50 m

Then, this is enough to answer the question. You need to use this formula:

d = v_0 * t + ½ * a * t²

Given the values, solve for a.

 

Oops. My bad. Then, we have...

s = 50 + v_0t + ½at²

Good thing you catch that mistakes! Without you, I would not notice the mistakes I make!

 

s is the displacement
a is acceleration

 

Oops. Sorry about that.

Hm... Before 20 seconds, we know that:

→the rocket is 50 m above the ground.
→v_0 = 0
→v_f = ?
→a > 0
→t = 20

So you use this form d_1 = h_0 + v_0 * t + ½ * a * t² = ½ * a * t². Clearly, d_1 =50 + ½ * a * t².

Between 20 and 30 seconds, since the rocket coasts up, we can say that a = 0, and that v_0_n = some velocity. Also, we need to determine the time interval between 30 seconds and 20 seconds; otherwise, if you just let t = 30, then you are answering the question wrong. It's after 20 seconds, we have the rocket having the zero acceleration and constant velocity (so that is the 10 second difference.). We should get:

d_2 = v_0_2 * Δt [where Δt is the difference between the time periods.]

Add up the distance and set that equal to 8000. We obtain:

d_1 + d_2 = 8000
50 + ½ * a * 20² + v_0_n * 10 = 8000
½ * a * 20² + v_0_n * 10 = 7950

Actually, you are correct. This problem seems to be impossible to solve!

 

Then, it's just this:

½ * a * 20² + v_0_n * 10 = 8000

All we have is just a/30 = (sum of all accelerations = a + 0)/(10 + 20).

At the first 20 seconds, a > 0. Then, after 20 seconds, a = 0.

 

Oh! I forgot to mention. Between t = 20 and t = 30, we have the same velocity as usual (rocket coasting up). This goes the same after the acceleration at t = 20. Use the acceleration formula: a = v_f/t, so we have...

½ * v_f/20 * 20² + v_f * 10 = 8000

Solve for v_f and find a using a = v_f/(overall time elapsed) = v_f / 30.