Acceleration–time graphs Transitional Reasoning Practice

Questions

1. 1.

   A sensor-monitored cart travels along a straight track with an initial velocity of $-4\text{ m/s}$ at $t = 0\text{ s}$. Its acceleration–time data shows a constant acceleration of $+2\text{ m/s}^2$ from $t = 0\text{ s}$ to $t = 4\text{ s}$, followed by a constant acceleration of $-1\text{ m/s}^2$ from $t = 4\text{ s}$ to $t = 8\text{ s}$. Based on this acceleration–time profile, which statement correctly describes the cart's motion?

   • A) The cart travels in the negative direction throughout the entire 8-second interval.
   • B) The cart increases its speed continuously from $t = 0\text{ s}$ to $t = 4\text{ s}$.
   • C) The cart reverses its direction of travel at $t = 2\text{ s}$ and comes to rest at $t = 8\text{ s}$.
   • D) The cart experiences a net change in velocity of zero over the entire 8-second duration.
2. 2.

   An autonomous inspection robot travels along a straight path with an initial velocity of $+12\text{ m/s}$ at $t = 0\text{ s}$. Its sensor logs a two-stage acceleration profile: a constant acceleration of $-5\text{ m/s}^2$ from $t = 0\text{ s}$ to $t = 4\text{ s}$, followed by a constant acceleration of $+3\text{ m/s}^2$ from $t = 4\text{ s}$ to $t = 10\text{ s}$. Based on this acceleration–time record, at what time does the robot first momentarily come to rest, and what is its velocity at $t = 10\text{ s}$?

   • A) At $t = 2.0\text{ s}$, and $+8\text{ m/s}$
   • B) At $t = 4.0\text{ s}$, and $-8\text{ m/s}$
   • C) At $t = 2.4\text{ s}$, and $+6\text{ m/s}$
   • D) At $t = 2.4\text{ s}$, and $+10\text{ m/s}$

Answers and step-by-step solutions appear after you finish the test.