In which of the following situations is the distance traveled proportional to $t$?

• A. An object moves with speed that increases linearly with $t$.
• B. An object moves in a circle at constant speed.
• C. An object moves at constant speed along a straight line.
• D. An object accelerates uniformly from rest.

Answer: (C)

Verified step by step guidance

1. Understand that distance traveled is proportional to time (t) when the speed is constant, meaning the object covers equal distances in equal time intervals.
2. Analyze the first situation: speed increases linearly with time, so speed is not constant; distance will depend on the integral of speed over time, which is proportional to \( t^2 \), not \( t \).
3. Consider the second situation: an object moves in a circle at constant speed, so the distance along the circular path is proportional to time, but the displacement is not; however, the problem asks about distance traveled, so this could be proportional to \( t \).
4. Look at the third situation: an object moves at constant speed along a straight line, so distance traveled is directly proportional to time, \( d = vt \), where \( v \) is constant.
5. Examine the fourth situation: an object accelerates uniformly from rest, so speed increases linearly with time, and distance traveled is proportional to \( t^2 \) (using \( d = \frac{1}{2}at^2 \)), not \( t \).