Instantaneous Velocity vs Average Velocity: Expert Solutions for Success

Instantaneous Velocity vs. Average Velocity

Introduction

Average velocity is given by the change in displacement of an object over a given time interval while on the other hand, the instantaneous velocity is given by the specific rate of change of displacement. In a graph, the average velocity is given by the slope of the straight line joining the two given points. Instantaneous velocity on the other hand is the slope of a tangent line that passes through the point of interest. The objective of this lab is to find the average and instantaneous velocities of a glider sliding over an air track. 

Question 1

Data and Analysis

Table 1: table of displacement, D (cm), time of travel, and the average velocity of the glider

D (cm)	t1 (s)	t2 (s)	t3 (s)	t4 (s)	t5 (s)	tavg (s)	vavg (cm/s)
130	2.61	2.61	2.60	2.60	2.61	2.61	49.90
120	2.34	2.34	2.34	2.34	2.34	2.34	51.26
110	2.13	2.12	2.11	2.11	2.11	2.12	51.95
100	1.85	1.84	1.84	1.84	1.84	1.84	54.23
90	1.70	1.70	1.70	1.70	1.70	1.70	53.02
80	1.50	1.50	1.49	1.49	1.50	1.49	53.51
70	1.29	1.29	1.29	1.29	1.29	1.29	54.40
60	1.09	1.09	1.09	1.09	1.09	1.09	55.01
50	0.91	0.91	0.91	0.91	0.91	0.91	54.76
40	0.72	0.71	0.70	0.70	0.70	0.71	56.64
30	0.54	0.54	0.54	0.54	0.54	0.54	55.70
20	0.35	0.35	0.35	0.35	0.35	0.35	56.91
9.99	0.17	0.17	0.17	0.17	0.17	0.17	57.81
						Average Velocity	54.24

To find the average time the following formula was used

For example, when D = 130 cm, the average time was calculated as

The above method was used when calculating the average velocities for the other values of D and the results entered in table 1 above.

On the other hand, to get the average velocity the following formula was used

For example, when D = 100 cm, the average velocity was found to be

 

Figure 1: graph of position of glider versus time taken to cover the displacement

 

Question 2

From the equation of the graph in figure 1, the instantaneous velocity at x1 is given by the derivative of the equation

Therefore, the instantaneous velocity is 52.74 cm/s.

 

Question 3

 

Discussion

As seen from the graph in figure 1, and the value of average velocity obtained through the calculation, we can say that the slope of the graph in figure 1 is the average velocity of the glider. The magnitude of the slope and the average velocity are approximately equal although there is an error of 2.77%. Some of the possible causes of errors are such as inconsistent times for the same displacement which might have been caused by not starting the glider from the same position for the same displacement. Another possible cause of the error is the slight rotation of the glider flag or giving the glider a slight push when releasing it. Also, placing the photo-gates at exactly D/2 position might not have been done thus causing errors in the measurement.

 

As shown in Table 1 above, the average velocity of the glider was increasing as the displacement D decreased. Since the air track was inclined, the average velocity of the glider was increasing as it approached the lowest point. This is because of the acceleration due to gravity acting on the glider which makes the glider move faster as it nears the lower end than it was at the upper end.