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velocity, acceleration, distance

Hello I need help with the following Physics problems.

9. A train approaches a small town with a constant velocity of +28.6 m/s. The operator applies the brake, reducing the train's velocity to +11.4 m/s. If the average acceleration of the train during brake is -1.35 m/s^2. For what elapsed time does the operator apply the brake?
10. Two cars travel along a level highway. It is observed that the distance between the card is increasing. Which one of the following statements concerning this situation is necessarily true?
11. A car, starting from rest, accelerates in a straight-line path at a constant rate of 2.5m/s^2. How far will the car travel in 12 seconds?
12. The minimum takeoff speed for a certain airplane is 75 m/s. What minimum acceleration is required if the plane must leave a runway of length 950 m? Assume the plane starts from rest at one end of the runway?
13. A car traveling along a rod begins accelerating with a constant acceleration of1.5m/s^2 in the direction of motion. After traveling 392 m at this acceleration, its speed is 35 m/s. Determine the speed of the car when it began accelerating.
14. A ball is thrown vertically upward from the surface of the earth. Consider the following quantities: (1) the speed of the ball; (2) the velocity of the ball; (3) the acceleration of the ball.
Which of these is zero when the ball has reached the maximum height?
15. A ball is dropped from rest from a tower and strikes the ground 125 m below. Approximately how many seconds does it take the ball to strike the ground after being dropped?
16. Elijah throws a tennis ball vertically upward. The ball returns to the point of release after 3.5 s. What is the speed of the ball as it is released?
An object is moving along the x axis. The graph shows its position from the starting point as a function of time. Various segments of the graph are identified by the letters A, B, C, and D.
17. During which interval is the object moving in the negative x direction?
18. What is the velocity of the object at t = 7.0 s?
19. What is the acceleration of the object at t = 7.0 s?


Solution Preview

Please see the attached file.

9. Average acceleration = change in velocity / time interval
Change in velocity = vf - vi = 11.4 - 28.6 = -17.2 m/s
Time =
Answer: (b)

10. (e).
The easiest way is assuming the two cars have constant velocities. However, the leading car travels at higher speed, 60 mph. the trailing car travels at lower speed, 40 mph. Then the distance between the cars is increasing. So we know that a, b, c, and d are not true.
However, both cars could be accelerating at the same time. Still, the two cars have the above initial velocity. The leading car accelerates faster than the trailing car. So ...

Solution Summary

The velocity, acceleration and distance of the motion are investigated. The solution is detailed and was rated '5/5' by the student who posted the question.