Acceleration, Velocity and Time

Acceleration, Velocity and Time#

For this problem, refer to the following figure.

Top: The x-component of a velocity vs. time graph is shown for an object:

The top graph is velocity vs time of an object where at t=0 the velocity is negative 1, from t=1 to t=1.5 the velocity is negative 2, at t=2 the velocity is 0. After t=2 the velocity continually increases.

Bottom: Below are possible options of that same object’s “acceleration vs. time” graph:

There are 5 graphs depicted below the velocity vs time graph. The 5 graphs depict acceleration vs time and are labelled A through E. Graph A is the same shape as the top graph. Graph B shows a negative acceleration from t=0 to t=1 and a positive acceleration from t=1.5 onwards. Graph C shows a positive acceleration from t=0 to t=1 and a negative acceleration from t=1.5 onwards. Graph D shows a negative acceleration curve that reaches the lowest at around t=2 and is 0 at t=3. Graph E shows increasing positive acceleration from t=0 to t=1, from t=1.5 and onwards the acceleration decreases.

Part 1#

Of the listed acceleration vs. time graphs shown in the bottom figure, which is consistent with the velocity vs. time graph shown in the top figure?

Answer Section#

  • Option A

  • Option B

  • Option C

  • Option D

  • Option E

Part 2#

If the initial position of the object whose velocity vs. time graph is shown in the figure (Top) is \(x_0\) = 0 \(m\), at what time does the object return to the position \(x\) = 0 \(m\) ?

Answer Section#

  • Never

  • 3.225 \(s\)

  • 1.5 \(s\)

  • 2 \(s\)

  • 2.866 \(s\)

Attribution#

Problem is licensed under the CC-BY-NC-SA 4.0 license.
The Creative Commons 4.0 license requiring attribution-BY, non-commercial-NC, and share-alike-SA license.