Answer:
(c) going around a circular track at a steady 100 miles per hour.
Explanation:
The acceleration of an object is equal to the rate of change of velocity of the object:
[tex]a=\frac{\Delta v}{\Delta t}[/tex]
where
[tex]\Delta v[/tex] is the change in velocity of the object
[tex]\Delta t[/tex] is the time interval
We notice that velocity is a vector, so it has both a magnitude and a direction. This means that [tex]\Delta v[/tex], the change in velocity, is either caused by a change in magnitude of velocity, or by a change in the direction.
Therefore, the acceleration is non-zero if at least one of the two is verified:
- There is a change in magnitude of the velocity
- There is a change in direction
Let's now analyze the three statements:
(a) traveling on a straight, flat road at 50 miles per hour. --> here there is no change in magnitude or direction of the velocity, so there is no acceleration.
(b) traveling on a straight uphill road at 30 miles per hour. --> here there is no change in magnitude or direction of the velocity, so there is no acceleration.
(c) going around a circular track at a steady 100 miles per hour. --> here there is no change in magnitude of the velocity, but the direction is changing (circular track), therefore there is acceleration.
