Acceleration–time graphs Knowledge-Based Practice

Questions

1. 1.

   An object initially at rest moves along a straight line. If its acceleration–time graph lies entirely above the time axis but slopes downward toward zero, which statement correctly describes its velocity during this interval?

   • A) The velocity decreases throughout the interval because the slope of the graph is negative.
   • B) The velocity increases throughout the interval, but at a decreasing rate.
   • C) The velocity remains constant throughout the interval because the acceleration approaches zero.
   • D) The velocity increases initially and then decreases as the acceleration approaches zero.
2. 2.

   Two objects, X and Y, move along a straight line with the same initial velocity at $t = 0$. If the area between the acceleration–time graph and the time axis from $t = 0$ to $t = t_1$ is greater for object X than for object Y, which of the following statements must be true at $t = t_1$?

   • A) Object X has a greater velocity than object Y.
   • B) Object X has traveled a greater distance than object Y.
   • C) Object X has a greater instantaneous acceleration than object Y.
   • D) Object X has a greater average velocity than object Y over the interval.
3. 3.

   An object moves along a straight line with an acceleration that is positive during the time interval from $t = 0$ to $t = t_1$ and negative from $t = t_1$ to $t = t_2$. At which point in time is the velocity of the object at its maximum value?

   • A) At $t = 0$
   • B) At $t = \frac{t_1}{2}$
   • C) At $t = t_1$
   • D) At $t = t_2$
4. 4.

   An object moves along a straight line over a time interval from $t_1$ to $t_2$. If the net area between its acceleration–time graph and the time axis over this interval is zero, which of the following statements must be true?

   • A) The object returns to its starting position at $t_2$.
   • B) The object remains at rest throughout the entire interval.
   • C) The object's average velocity over the interval is zero.
   • D) The object's velocity at $t_2$ is equal to its velocity at $t_1$.
5. 5.

   If the acceleration–time graph of an object moving in a straight line lies along the time axis ($a = 0$) throughout a given interval, which statement correctly describes its motion during that interval?

   • A) The object must remain stationary throughout the entire interval.
   • B) The object moves with a constant velocity throughout the interval.
   • C) The object moves with a steadily increasing speed throughout the interval.
   • D) The object's total displacement over the interval must be zero.
6. 6.

   An object moves along a straight line in the positive direction. If its acceleration–time graph is a horizontal line located below the time axis throughout an interval, how does the object's speed change during this interval?

   • A) Its speed increases at a constant rate.
   • B) Its speed remains constant.
   • C) Its speed decreases at a constant rate.
   • D) It immediately comes to a complete stop.
7. 7.

   An object moves along a straight line such that its velocity increases at a constant rate over time. Which of the following correctly describes the appearance of its acceleration–time graph over this interval?

   • A) A horizontal line segment at a constant non-zero value above the time axis
   • B) A straight line segment sloping upward from the origin with a constant positive slope
   • C) A horizontal line segment lying directly along the time axis at zero
   • D) A parabolic curve that curves upward with increasing time
8. 8.

   An object moves along a straight line, and its acceleration–time graph is known across a given time interval. Which of the following quantities cannot be determined from this graph alone without knowing an initial condition?

   • A) The change in the object's velocity over the interval
   • B) The instantaneous acceleration of the object at any given moment
   • C) The time intervals during which the acceleration remains constant
   • D) The instantaneous speed of the object at any given moment
9. 9.

   What physical quantity is represented by the area between an object's acceleration–time graph and the time axis over a given time interval?

   • A) The displacement of the object
   • B) The rate of change of acceleration
   • C) The instantaneous velocity at the end of the interval
   • D) The change in the object's velocity
10. 10.

    A toy car moves along a straight line with an initial velocity of $6\text{ m/s}$ at $t = 0\text{ s}$. If its acceleration–time graph shows a constant acceleration of $2\text{ m/s}^2$ over the interval from $t = 0\text{ s}$ to $t = 4\text{ s}$, what is the car's velocity at $t = 4\text{ s}$?

    • A) $8\text{ m/s}$
    • B) $10\text{ m/s}$
    • C) $14\text{ m/s}$
    • D) $40\text{ m/s}$

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