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 x 1 , x 2 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 v 1i , v 1f , v 2i , v 2f is zero Two vectors showing the directions of the car's acceleration during the first and second intervals a 1 , a 2 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 a 1 (3 51 m s 2 ) to a final velocity v 1f (23 1 m s) No calculations, just list your random for this question, by description symbol (3) Interval 1 Calculate the car's displacement x 1 for the first interval without calculating t 1 first Check use x 1 to calculate a 1 or v 1f , and verify that they come out right (4) Interval 1 Calculate how much time t 1 it takes the car to speed up Check put your t 1 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 a 2 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

The Answer is in the image, click to view ...

Answered step by step

Verified Expert Solution

Link Copied!

Question

1 Approved Answer

Posted on Jun 22, 2024

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:
1. 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
2. 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 v_1i, v_1f, v_2i, v_2f is zero
3. 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 v_1f (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 v_1f, 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?