61 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= 30 sec is 0.238 m/s. Assume all values are known to 3 significant figures 

Step-by-Step Solution

Answer

The velocity is approximately the value 0.233 m/s

Graph and its analysis

To analyses 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.

Calculating the velocity at t = 30.0 s

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

Coordinate \(\left( {30,9} \right)\)  and \(\left( {60,16} \right)\) 

Slop of the line will be

\[\begin{array}{l}m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_2}}}\\Here\,the\,coordinates\,are\,(30,9)\,\,\,and\,\,\,(60,16)\\m = \frac{{16 - 9}}{{60 - 30}}\\m = 0.233\,m/s\end{array}\]
 

Hence the velocity is approximately to the value \[0.233 m/s\]