62 P E - College Physics (Urone)

Question

By taking the slope of the curve in Figure 2.63, verify that the acceleration is 3.2 m/s² at t = 10 s.

Step-by-Step Solution

Answer

The acceleration is approximately to the value 4.12 m/s².

Creating the graph and its analysis

To analyze movement, motion graphs can be employed.

The mathematical approaches and graphical solutions for determining motion equations are the same.

The slope of a graph of displacement x vs. time t represents velocity v.

The inclination of a graph of velocity v vs. time t is called acceleration.

Average velocity, instantaneous velocity, and acceleration can all be calculated using graphs.

Calculation of acceleration at t = 10.0 s

Here if we carefully look into the figure, in your text book let’s take any two points on the line 

Coordinate (0,175) and (30,300)

Slop of the line will be

\[m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_2}}}\]

Here the coordinates are \(\left( {0,175} \right)\) and \(\left( {30,300} \right)\) 

\[\begin{array}{l}m = \frac{{300 - 175}}{{30 - 0}}\\m = 4.16\,m/{s^2}\end{array}\]
 

Hence the acceleration is approximately to the value\[4.12 m/{s^2} \].