Question

your answer is incorrect.
consider the position versus time and velocity versus time graphs for an object in motion. which one of the following phrases best describes the motion of the object?
position vs time graph (x in m, t in s) and speed vs time graph (v in m/s, t in s) are shown
options:

• constant position
• constant speed
• constant velocity
• constant acceleration
• none of the above

Explanation:

1. Analyze "constant position": A constant position would mean the position - time graph is a horizontal line (no change in position over time). But the position - time graph here is curved and increasing, so this is incorrect.
2. Analyze "constant speed": A constant speed would mean the velocity - time graph is a horizontal line (since speed is the magnitude of velocity). The velocity - time graph here is a straight line with a positive slope, so speed is changing, so this is incorrect.
3. Analyze "constant velocity": Constant velocity means both speed and direction are constant. For velocity to be constant, the velocity - time graph should be horizontal (constant speed) and the position - time graph should be a straight line (constant slope, which implies constant velocity). The velocity - time graph here has a slope (so speed is changing), so velocity is not constant, so this is incorrect.
4. Analyze "constant acceleration": Acceleration is the rate of change of velocity. The velocity - time graph is a straight line, which means the slope (acceleration) is constant. The position - time graph is a curve (which is consistent with changing velocity, as the second derivative of position with respect to time is acceleration, and a curved position - time graph has a changing first derivative (velocity) and a constant second derivative (acceleration) when the velocity - time graph is linear). So this option is correct.
5. "None of the above" is incorrect because we have identified that the object has constant acceleration.

Answer:

D. constant acceleration