---
title: "A small remote-controlled car travels along a straight track. The velocity of the car as a function of time is shown in the provided graph. At which of the following times is the velocity of the car changing at the fastest rate?"
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url: "https://nerd-notes.com/ubq/113080/"
date_modified: "2026-05-05T03:45:56+00:00"
---

# A small remote-controlled car travels along a straight track. The velocity of the car as a function of time is shown in the provided graph. At which of the following times is the velocity of the car changing at the fastest rate?

A small remote-controlled car travels along a straight track. The velocity of the car as a function of time is shown in the provided graph. At which of the following times is the velocity of the car changing at the fastest rate?

![A velocity versus time graph. The vertical axis is velocity v in meters per second (m/s) ranging from 0 to 12. The horizontal axis is time t in seconds (s) ranging from 0 to 10. A smooth curve starts at (0,0). From t=0 to t=2, the curve is concave up with a small increasing slope. At t=3, the curve reaches its steepest positive slope. From t=4 to t=8, the curve is concave down as the slope decreases toward zero. From t=8 to t=10, the curve is a horizontal line at v=10 m/s. Four points are labeled on the curve: Point A at t=1 s, Point B at t=3 s, Point C at t=6 s, and Point D at t=9 s.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-v-t-graph-1777952756-d278uf.jpg)

- **A.** At \(t = 1 \text{ s}\), because the car has moved the shortest distance from its starting position.
- **B.** At \(t = 3 \text{ s}\), because the slope of the velocity-time graph has its maximum magnitude at this instant.
- **C.** At \(t = 6 \text{ s}\), because the velocity of the car is still increasing toward its maximum value.
- **D.** At \(t = 9 \text{ s}\), because the car is traveling with its greatest speed at this time.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/113080/*