? For this assignment, we will consider the motion of two spaceships in space; we assume they are point particles. Let the position vector at some time t of one of the spaceships be r1(t), while that of the other spaceship be r2(t). Suppose that the acceleration of spaceship 1 is a1 = 2ˆi + 1ˆj + 3kˆ and that of spaceship 2 be a2 = 2ˆi − 1ˆj + 3kˆ, where ˆi, ˆj, and kˆ are unit vectors in the x, y and z directions respectively.
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A. Is the acceleration of either spaceships uniform or nonuniform?
B. What is the instantaneous velocity of spaceship 1 and spaceship 2?
C. What are their position vectors? Will the spaceships collide assuming that spaceship 1 starts at point with position vector r1,0 = 1ˆi + 1ˆj + 1kˆ and spaceship 2 starts at r2,0 = 1ˆi − 1ˆj + 1kˆ.
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A. What velocity does spaceship 2 have 10 seconds after it starts to move?
B. How far would spaceship 2 have travelled in this 10 seconds?
C. How far would spaceship 1 have travelled in this 10 seconds as well?
D. What is the average velocity of spaceship 1 after 20 seconds of travel?
E. What is the average acceleration of spaceship 2 after 20 seconds of travel?
F. Sketch an acceleration-time graph for the two spaceships.
G. Assuming that spaceship 1 has the acceleration in the preamble for 15 seconds, then it travels at a constant velocity for another 20 seconds and it accelerates with the same acceleration as before for 10 seconds, what would a velocity-time graph of this motion look like? Just a sketch is fine. Remember to show what velocity it has at the end of the 10 seconds.