Graphing Position, Velocity, and Acceleration Graphs Practice Problems

A frictionless trolley follows a straight line path as shown in the figure below. Represent its motion using position-versus-time, velocity-versus-time, and acceleration-versus-time graphs. Assume s = 0 at the point where the trolley is shown.

On a racing circuit, John is cruising at a constant 121 km/h. Micheal starts from rest (maintaining constant acceleration) and catches John within 968 meters. Qualitatively draw the position vs. time graph for both cars from John's start to the point where he catches up.

A moving particle's position is described by the equation 𝑦 = 15 + 8𝑡 − 3𝑡³, where 𝑡 is measured in seconds and 𝑦 is measured in meters. Plot the position of 𝑦 as a function of time 𝑡 from 𝑡 = 0 to 𝑡 = 4.0 s.

A cyclist begins her journey from rest at t = 0 and moves in a straight line. The displacement of the cyclist throughout the journey is given in the following table. Determine:

(a) The average velocity over time

(b) The velocity-time graph

A surveillance camera captures images of a bicycle moving along a path at intervals of 15 seconds. A distance scale is provided in the footage with the velocity of the bicycle. Construct a position-versus-time graph for the bicycle using the data from the surveillance footage.

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The position-time graph of a moving vehicle is shown below. What will the velocity-time graph of the vehicle look like for the given interval?

Sam & Dean are walking in a straight path. Sam is located x = 8 km away from the start point at t = 0 hr. He walks constantly at 4 km/hr. Dean started from the start point at t = 1 hr and walks constantly at 6 km/hr.

Draw a position-versus-time graph showing the motion of both Sam & Dean.

A train begins moving from rest at t = 0 along a straight track. The following table provides its position over different intervals of time. Find the acceleration of the train over each interval and represent it graphically.