Suppose that an object is moving with constant nonzero acceleration. Which of the following is an accurate statement concerning its motion? (a) - In equal times its speed changes by equal amounts. (b) - In equal times its velocity changes by equal amounts. (c) - In equal times it moves equal distances. (d) - A graph of its position as a function of time has a constant slope. (e) - A graph of its velocity as a function of time is a horizontal line.

Answer: The right answer is b)

Explanation:

By definition, acceleration is the change in velocity (in module or direction) over a given time interval, as follows:

a = (v-v₀) / (t-t₀)

If we take t₀ = 0 (this is completely arbitrary), we can rewrite the equation above, as follows:

v = v₀ + at

We can recognize this function as a linear one, where a represents the slope of the line.

If a is constant, this means that the relationship between the change in velocity and the change in time remains constant, in other words, in equal times, its velocity changes in an equal amount.

Let's suppose that a = 10 m/s/s. (Usually written as 10 m/s²).

This is telling us that each second, the velocity increases 10 m/s.