60 PE - College Physics (Urone)

Question

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. 

Step-by-Step Solution

Answer

The velocity is approximately 0.217 m/s

Explaining motion graph and its analysis

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.

Calculating velocity at t = 10.0 sec

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 \[0.217 m/s\].