Using approximate values, calculate the slope of the curve in Figure 2.62 to verify that the velocity at t = 10 s is 0.208 m/s. Assume all values are known to 3 significant figures.

Motion graphs can be used to analyze movement.

Graphical solutions for determining motion equations are identical to mathematical methods.

Velocity v is the slope of a graph of displacement x vs. time t.

Acceleration is the inclination of a graph of velocity v vs. time t.

Graphs can be used to calculate average velocity, instantaneous velocity, and acceleration.

Here, we carefully look into the figure and take any two points on the line. We take

coordinates \(\left( {0,3} \right)\) and \(\left( {60,16} \right)\).

The slope of the line is

\[\begin{array}{l}m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_2}}}\\Here\,the\,coordinates\,are\,(0,3)\,\,\,and\,\,\,(60,16)\\m = \frac{{16 - 3}}{{60 - 0}}\\m = 0.21666\,\,m/{s^2}\end{array}\]

Hence the velocity is approximately \[0.217 m/s\].