Is it possible for velocity to be constant while acceleration is not zero? Explain.
No, it is not possible for velocity to be constant while acceleration is not zero.
The rate at which an object's velocity changes with respect to time is known as acceleration.
The item experiences acceleration whenever its velocity changes.
As a result, anytime the magnitude or direction of velocity changes, a non-zero value of acceleration is associated with it.
Acceleration is a vector quantity. Its direction and magnitude depend upon the velocity vector.
The direction of acceleration is the same as that of the change in velocity.
Hence if there is no change in velocity, there would not be acceleration.
Dragsters can actually reach a top speed of in only considerably less time than given in Example 2.10 and Example 2.11.
(a) Calculate the average acceleration for such a dragster.
(b) Find the final velocity of this dragster starting from rest and accelerating at the rate found in (a) for 402 m (a quarter mile) without using any information on time.
(c) Why is the final velocity greater than that used to find the average acceleration?
Hint: Consider whether the assumption of constant acceleration is valid for a dragster. If not, discuss whether the acceleration would be greater at the beginning or end of the run and what effect that would have on the final velocity.
Consider the velocity vs. time graph of a person in an elevator shown in Figure 2.58. Suppose the elevator is initially at rest. It then accelerates for, maintains that velocity for , then decelerates for until it stops. The acceleration for the entire trip is not constant so we cannot use the equations of motion from Motion Equations for Constant Acceleration in One Dimension for the complete trip. (We could, however, use them in the three individual sections where acceleration is a constant.) Sketch graphs of
(a) position vs. time and
(b) acceleration vs. time for this trip.
A student drove to the university from her home and noted that the odometer reading of her car increased by . The trip took .
(a) What was her average speed?
(b) If the straight-line distance from her home to the university is in a direction south of east, what was her average velocity?
(c) If she returned home by the same path after she left, what were her average speed and velocity for the entire trip?
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