(1 pt) Which of the following statements is true? (Give all correct answers, i.e., A, C, AE, ABCD . . .)
A) An object with a constant speed can not accelerate.
B) When the velocity is constant, the average velocity over any time interval can not differ from the instantaneous velocity at that instant.
C) If the acceleration of a body is constant as measured from a given reference frame, it is necessarily constant when measured from all other reference frames.
D) An object can have a zero velocity and still be accelerating.
E) The velocity of an object can reverse direction when its acceleration is constant.
A. could be true if it stated "constant velocity" can not accelerate, but constant speed, false.
B. Yes, true
C. If another reference frame is accelerating, then not true from that accelerating reference frame.
D. yes, true. Thnk of a baseball thrown up, at the very top, veloicty is zero.
E. yes, again, consider the baseball thrown up.
To determine which of the statements are true, let's go through each statement one by one and analyze them:
A) "An object with a constant speed can not accelerate."
To determine the truth of this statement, we need to understand the concepts of speed and acceleration. Speed refers to the rate at which an object covers distance, while acceleration refers to the rate at which the velocity of an object changes.
If an object has a constant speed, it means its distance covered per unit time remains the same. However, acceleration refers to a change in velocity, not speed. So, even if the speed is constant, the object can still accelerate if there is a change in its direction. For example, if the object is moving in a circular path at a constant speed, it is constantly changing its direction, and thus accelerating. Therefore, statement A is false.
B) "When the velocity is constant, the average velocity over any time interval can not differ from the instantaneous velocity at that instant."
To assess the truth of this statement, let's first understand the definitions of average velocity and instantaneous velocity. Average velocity is the total displacement of an object divided by the total time taken. Instantaneous velocity, on the other hand, refers to the velocity of an object at a specific instant in time.
If an object has a constant velocity, it means it consistently travels at the same speed and in the same direction. In this case, the average velocity over any time interval would be the same as the instantaneous velocity, as the object is not accelerating or changing its direction. Therefore, statement B is true.
C) "If the acceleration of a body is constant as measured from a given reference frame, it is necessarily constant when measured from all other reference frames."
To determine the truth of this statement, we need to consider the nature of acceleration and reference frames. Acceleration refers to the rate of change of velocity. Reference frames, on the other hand, are coordinate systems used to observe and measure the motion of objects.
If the acceleration of a body is constant in a given reference frame, it means the velocity of the body is changing by the same amount in the same direction per unit time. However, when measuring from different reference frames that are in relative motion with respect to each other, the observed acceleration may differ due to the perspective and relative velocities between the frames. Therefore, statement C is false.
D) "An object can have a zero velocity and still be accelerating."
To assess the truth of this statement, we need to understand the relationship between velocity and acceleration. Velocity refers to both the speed and direction of an object's motion, while acceleration refers to the rate of change of velocity.
An object can have a zero velocity if it is at rest or momentarily stopped. However, if there is a change in its velocity, i.e., a change in its speed or direction, it is considered to be accelerating. For instance, if an object is thrown up in the air, it will momentarily stop at its highest point but will continue to accelerate downwards due to the force of gravity. Therefore, statement D is true.
E) "The velocity of an object can reverse direction when its acceleration is constant."
To determine the truth of this statement, we need to examine the relationship between velocity, acceleration, and direction. Velocity includes both speed and direction, while acceleration refers to a change in velocity.
If an object's acceleration is constant and in a particular direction, it means the object's change in velocity is consistent in both magnitude and direction. However, if the object reverses its direction, it means its velocity changes direction completely, and thus, its acceleration cannot remain constant. Therefore, statement E is false.
In summary, the true statements are:
B) When the velocity is constant, the average velocity over any time interval cannot differ from the instantaneous velocity at that instant.
D) An object can have a zero velocity and still be accelerating.