Question

Group Activity In Exercises 5 and 6, the coordinates s of a moving body for various values of t are given. (a) Plot s versus t on coordinate paper, and sketch a smooth curve through the given points. (b) Assuming that this smooth curve represents the motion of the body, estimate the velocity at \(t=1.0, t=2.5,\) and \(t=3.5 .\) \(\frac{t(\mathrm{sec})}{s(\mathrm{ft})} \left| \begin{array}{ccccccccc}{0} & {0.5} & {1.0} & {1.5} & {2.0} & {2.5} & {3.0} & {3.5} & {4.0} \\ \hline s(\mathrm{ft}) & {12.5} & {26} & {36.5} & {44} & {48.5} & {50} & {48.5} & {44} & {36.5}\end{array}\right.\)

Short answer

By following these steps, one can sketch a motion graph and estimate velocities at specific points from the motion graph. Remember that exact values cannot be calculated as we are estimating from the graph.

Step-by-step solution

Plotting the motion graph

Start by organizing the time 't' and position 's' values in a table format. Then plot these points on a graph with time on the x-axis and distance on the y-axis. Use the points to sketch a smooth curve to represent the motion of the body.

Estimating the velocity at t=1.0, t=2.5, and t=3.5

Use the smooth curve to estimate the velocity at given times. Velocity is the derivative of the position function, so the velocity at each time point can be estimated by determining the slope of the tangent line to the curve at that point. At \(t=1.0\), check the slope at that point. Do the same for \(t=2.5\) and \(t=3.5\).

Interpreting the results

The values obtained for velocity signify the estimated speed of the moving body at the specified times. If there's a change in the direction of motion, the value of velocity will become negative. Hence, interpreting these values accurately helps understand the nature of the body's motion.