Proportional reasoning with motion | AP Physics | Khan Academy

What are the key assumptions made for the simplified model of spacecraft travel discussed in the video?

• Constant velocity, curved trajectory, non-zero initial velocity.

• Constant acceleration, straight-line path, zero initial velocity.

• Variable acceleration, straight-line path, non-zero initial velocity.

• Constant acceleration, curved trajectory, zero initial velocity.

If a spacecraft covers a certain distance in half the time compared to another mission, what is the relationship between its average velocity and the average velocity of the other mission? Assume constant acceleration and zero initial velocity for both.

• The average velocity is half.

• The average velocity is the same.

• The average velocity is twice.

• The average velocity is four times.

For a constant displacement, how does the average velocity of an object relate to the time it takes to cover that distance?

• Average velocity is directly proportional to time.

• Average velocity is inversely proportional to time.

• Average velocity is exponentially related to time.

• Average velocity is unrelated to time.

A spacecraft accelerates from rest over a certain distance. If a second spacecraft covers the same distance in half the time, how does its acceleration compare to the first spacecraft's acceleration?

• It is half the acceleration.

• It is four times the acceleration.

• It is twice the acceleration.

• It is one-fourth the acceleration.

For an object accelerating from rest over a fixed distance, if the time taken is tripled, how does its acceleration change?

• The acceleration becomes one-third of the original.

• The acceleration becomes three times the original.

• The acceleration becomes one-ninth of the original.

• The acceleration becomes nine times the original.

For an object accelerating from rest with constant acceleration, if the time of travel is reduced to one-third, how does the distance traveled change?

• The distance becomes one-third of the original.

• The distance becomes three times the original.

• The distance becomes one-ninth of the original.

• The distance becomes nine times the original.

A spacecraft accelerates from rest with a constant acceleration for a certain time, covering a distance X. If a second spacecraft accelerates from rest with the same constant acceleration for 50% more time, what distance does it cover?

• 1.5 times X

• 2.25 times X

• 0.67 times X

• 0.44 times X