PHYSICS 201: AVERAGE VELOCITY AND ACCELERATION EXERCISE
Solutions are shown in red.
The position of an object moving in one dimension is measured at certain times. The positions and times are recorded below.
(a) Find the average velocities between the measured times. Put your results in the table. Write in the best estimates for the times at which these velocities occur next to your velocity values.
(b) Find the average accelerations for the object. Put your results in the table. Write in the best estimates for the times at which these accelerations occur next to your acceleration values.
(c) Plot x vs. t. Connect the data points with straight line segments.
(d) Plot vx vs. t. (At what times do you plot your velocity values?) Note that the velocity values are the slopes of the straight line segments on the position graph. Connect the points with straight line segments.
(e) Plot ax vs. t. (At what times do you plot your acceleration values?) Note that the acceleration values are the slopes of the straight line segments on the velocity graph. Connect the points with straight line segments.
If we had more position values between t=0 and t=14 s, then we would have more velocity and acceleration values. These average velocities and accelerations would be better estimates of the velocities and accelerations experienced by the object. The plots would also have more line segments since there would be more points. Thus, the plots would appear smoother. Note that to get more position values between t=0 and t=14 s, we must take more measurements which decreases Dt. As Dt gets smaller and smaller, the plots get smoother, we get more and more values for average velocity and acceleration, and these values agree better and better with the actual velocities and accelerations experienced by the object at each instant in time. In the limit of Dt getting extremely small, the average velocities and accelerations are referred to as the instantaneous velocities and accelerations.