On a position-time graph for a particle, suppose the plot starts at some positive position and as the time goes on the curve gets steeper and steeper while curving upwards. Which of the following must be true?
a. The speed of the particle is constant. b. The acceleration of the particle is constant.
c. The speed of the particle is decreasing. d. The acceleration of the particle is positive.
[Ques. 2] A car is moving in the positive direction along a straight highway and accelerates at a constant rate while going from point A to point B. If the acceleration is positive, increasing the speed of the car, when does the position where the average speed equals the instantaneous speed occur during the time interval from A to B? Assume the time interval is T.
a. T/2 from the start of the interval b. before T/2 from the start of the interval
c. after T/2 from the start of the interval d. It depends on the speed at the start of the time interval.
[Ques. 3] A car is moving along a straight highway and accelerates at a constant rate while going from point A to point B. If the acceleration is positive, increasing the speed of the car, where does the position where the instantaneous speed equals the average speed occur for the interval from A to B?
a. midway between A and B b. closer to A than to B
c. closer to B than to A d. Any of the answers could be correct depending on the original speed.
[Ques. 4] An object moves at a constant velocity of 12 m/s to the southwest for an interval of 20 s. Halfway through this interval, what is the magnitude of its instantaneous velocity?
a. It can be any value from 0 to 24 m/s. b. 6 m/s
c. 12 m/s d. More information is needed.
[Ques. 5] A ball is pushed downhill with an initial velocity of 3.0 m/s. The ball rolls down a hill with a constant acceleration of 1.6 m/s2 . The ball reaches the bottom of the hill in 6.0 s. What is the ball's velocity at the bottom of the hill?
a. 10 m/s b. 13 m/s
c. 16 m/s d. 17 m/s
[Ques. 6] If a is acceleration, v is velocity, x is position, and t is time, then which equation is not dimensionally correct?
a. t = x/v b. a = v2/x
c. v = a/t d. t2 = 2x/a
[Ques. 7] Which formula is dimensionally consistent with an expression yielding a value for velocity? (a is acceleration, x is distance, and t is time)
a. v/t2 b. vx2
c. v2/t d. at
[Ques. 8] In which of the following cases is the displacement's magnitude half the distance traveled?
a. 10 steps east followed by 3 steps west
b. 28 steps east followed by 14 steps west
c. 6 steps east followed by 24 steps west
d. 12 steps east followed by 4 steps west
e. 5 steps east followed by 25 steps west
[Ques. 9] Starting from rest, a car accelerates down a straight road with constant acceleration a for a time t, then the direction of the acceleration is reversed, (i.e., it is a), and the car comes to a stop in an additional time t, the time for the whole trip being 2t. At what time, or times, is the average velocity of the car for the trip equal to its instantaneous velocity during the trip?
a. There is no such time.
b. It is at the halfway point at t.
c. This occurs at 2 times, 0.5t and 1.5t.
d. This occurs at 2 times, 0.707t and 1.293t.
[Ques. 10] The slope of the acceleration vs. time curve represents
a. the velocity.
b. the rate of change of acceleration.
c. the rate of change of displacement.
d. the area under the position vs. time curve.
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