Understanding Motion: Velocity and Acceleration

What statement below about the recorded velocity and acceleration is correct for a speeding up object moving towards the sensor?

a. The recorded values of both, the velocity and acceleration are positive.
b. The recorded values of both, the velocity and acceleration are negative.
c. The recorded values of velocity are positive while the values of the acceleration are zero.
d. The recorded values of velocity are negative but the recorded values of acceleration are positive.
e. The recorded values of velocity are positive but the recorded values of acceleration are negative.

Answer:

For an object moving towards the sensor and speeding up, both its velocity and acceleration would be recorded as negative, making option B the correct answer.

Explanation: In understanding the motion of an object and its relationship between velocity and acceleration, one has to understand the assigned directionality. In the framework of this question, it's stated that the sensor identifies the direction away from it as positive. Therefore, an object moving towards the sensor would move in a negative direction. When an object is speeding up, its acceleration is in the same direction as its velocity.

Given these considerations, for an object moving towards the sensor and speeding up, its velocity would be negative (since it's moving in the direction opposite to what's considered positive) and its acceleration would also be negative (since it's speeding up in that same negative direction). Hence, the correct statement is b. The recorded values of both, the velocity and acceleration are negative.

This means the object would have a negative velocity (moving towards the sensor) and a negative acceleration (speeding up in the direction of the sensor).