Question

A student calculated the final velocity of a train that decelerated from 30.5 m/s and got an answer of −43.34 m/s. Which of the following might indicate that he made a mistake in his calculation?

a) The negative sign indicates a deceleration, so the calculation is correct.

b) The final velocity should be greater than the initial velocity.

c) The units of velocity are incorrect.

d) The train's acceleration is not considered in the calculation.

Answer 1

The correct answer that indicates a mistake in the student's calculation is option b) The final velocity should be greater than the initial velocity. The negative sign in a velocity value indicates direction, not magnitude. The units of velocity are correct, and including the train's acceleration is not necessary to determine if a mistake was made.

Step-by-step explanation:

The correct answer that indicates a mistake in the calculation is b) The final velocity should be greater than the initial velocity. When an object decelerates, its final velocity is always lower than its initial velocity. Therefore, a negative final velocity indicates that the train has decelerated correctly and the calculation is accurate.

The negative sign in a velocity value indicates the direction, not the magnitude of the velocity. In this case, the negative sign indicates that the train is moving in the opposite direction to its initial velocity. It does not indicate an error in the calculation.

The units of velocity are correct (m/s), so option c) is not the indication of an error. The calculation might consider the train's acceleration or deceleration, but it is not necessary to determine if a mistake was made in the calculation. Therefore, d) is also not the correct answer.