Question
This assignment is about a car moving along a straight line, which we'll take to be the x axis. The car speeds up from rest
This assignment is about a car moving along a straight line, which we'll take to be the x axis. The car speeds up from rest to some maximum velocity, then brakes down to a lower velocity, always moving from left to right.
- Make a diagram from the description in the previous paragraph, with an x axis from left to right. Draw:
- the car at the beginning (far left), again at the instant when it begins braking, and at the end (far right) two vectors (arrows), showing the car's displacement for each interval: x1, x2
- Three velocity vectors, to show the car's velocity at the beginning or end of each interval. Only three, though, since one of the velocities v1i, v1f, v2i, v2f is zero
- Two vectors showing the directions of the car's acceleration during the first and second intervals: a1, a2 Check: If your diagram doesn't have seven separate labeled vectors (arrows), it's not complete.
(2) Interval 1: the car speeds up from rest at a constant rate a1 (3.51 m/s2) to a final velocity v1f (23.1 m/s). No calculations, just list your random for this question, by description & symbol.
(3) Interval 1: Calculate the car's displacement x1 for the first interval without calculating t1 first.
Check: use x1 to calculate a1 or v1f, and verify that they come out right.
(4) Interval 1: Calculate how much time t1 it takes the car to speed up. Check: put your t1 back into the original eqn, or better yet a different one, and see if things come out right.
(5) Interval 2: immediately upon reaching the velocity chosen in #2, the driver brakes until the car's velocity is 13.4 m/s, having traveled another 73.1 m while braking. List your random by description & symbol.
(6) Interval 2: Calculate the car's acceleration a2 while braking. Check: put this acceleration back into the original or another eqn, see if you get the right value(s) for one or more of your random.
(7) Now consider intervals 1 and 2 as sub-intervals of one big interval during which the car speeds up from rest, then slows down to the velocity chosen in #5. Calculate the car's average velocity for the entire big interval.
(8) Calculate the car's average acceleration for the entire big interval.
Checks: how should the overall average velocity and average acceleration compare to the velocities and accelerations seen during each interval?
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