Acceleration–time graphs Transitional Reasoning Download PDF

Questions

1. 1.

   An autonomous freight capsule moves along a straight horizontal track. Telemetry records its acceleration over a 9-second run: it maintains a constant acceleration of $+2\text{ m/s}^2$ from $t = 0\text{ s}$ to $t = 5\text{ s}$, followed immediately by a constant acceleration of $-5\text{ m/s}^2$ from $t = 5\text{ s}$ to $t = 9\text{ s}$. If the capsule momentarily comes to rest at $t = 9\text{ s}$, what was its initial velocity at $t = 0\text{ s}$, and during which interval was its speed continuously decreasing?

   • A) $+10\text{ m/s}$, and between $t = 5\text{ s}$ and $t = 9\text{ s}$
   • B) $+10\text{ m/s}$, and between $t = 0\text{ s}$ and $t = 5\text{ s}$
   • C) $-10\text{ m/s}$, and between $t = 5\text{ s}$ and $t = 9\text{ s}$
   • D) $-10\text{ m/s}$, and between $t = 0\text{ s}$ and $t = 5\text{ s}$
2. 2.

   An automated inspection shuttle moves along a straight track, starting from rest at the origin at $t = 0\text{ s}$. On its acceleration–time graph, the acceleration increases linearly from $0\text{ m/s}^2$ to $+6\text{ m/s}^2$ between $t = 0\text{ s}$ and $t = 4\text{ s}$, and then remains constant at $-3\text{ m/s}^2$ from $t = 4\text{ s}$ to $t = 8\text{ s}$. Which statement correctly describes the shuttle's velocity at $t = 8\text{ s}$ and its position relative to the origin?

   • A) Its velocity is $+6\text{ m/s}$, and it is located at the origin.
   • B) Its velocity is $0\text{ m/s}$, and it is located ahead of the origin.
   • C) Its velocity is $0\text{ m/s}$, and it has returned to the origin.
   • D) Its velocity is $-12\text{ m/s}$, and it is located behind the origin.
3. 3.

   A sensor-equipped test vehicle travels along a straight east-west track, with east defined as the positive direction. Starting with an initial velocity of $+12\text{ m/s}$ at $t = 0\text{ s}$, it moves with a constant acceleration of $-4\text{ m/s}^2$ from $t = 0\text{ s}$ to $t = 4\text{ s}$, followed immediately by a constant acceleration of $+3\text{ m/s}^2$ from $t = 4\text{ s}$ to $t = 7\text{ s}$. Based on this acceleration–time data, what is the vehicle's velocity at $t = 7\text{ s}$, and at what instant does it reverse its initial direction of motion?

   • A) $+9\text{ m/s}$, reversing direction at $t = 4\text{ s}$
   • B) $+5\text{ m/s}$, reversing direction at $t = 3\text{ s}$
   • C) $-4\text{ m/s}$, reversing direction at $t = 3\text{ s}$
   • D) $+5\text{ m/s}$, reversing direction at $t = 4\text{ s}$