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Compute your average speed in the following two cases. (a) You walk 240 ft at a speed of 4.0 ft/s and then run 240 ft at a speed of 10 ft/s along a straight track. (b) You walk for 1.0 min at a speed of 4.0 ft/s and then run for 1.0 min at 10 ft/s along a straight track.

Compute your average speed in the following two cases. (a) You walk 240 ft at a speed of 4.0 ft/s and then run 240 ft at a speed of 10 ft/s along a straight track. (b) You walk for 1.0 min at a speed of 4.0 ft/s and then run for 1.0 min at 10 ft/s along a straight track.

Grade:11

2 Answers

Aditi Chauhan
askIITians Faculty 396 Points
9 years ago
Let us assume that distance you walk with speed v1 is s1 while the distance you run with speed v2 is s2.
We also assume that the time taken to travel distance s1 with speed v1 is t1 whereas the time taken to travel distance s2 with speed v2 is t2.
(a) Given:
Distance travelled while walking, s1 = 240
Speed with which distance s1 was travelled, v1 = 4.0 ft/s
Distance travelled while running, s2 = 240 ft
Speed with which distance s2 was travelled, v2 = 10 ft /s
The average speed is given as:
average\ speed\ \frac{total distance\ travelled}{elapsed\ time}

The total distance that you travel is the sum of distance s1 and s2 whereas the elapse time is the sum of time t1 and t2.
Therefore, the average speed is:
average\ speed = \frac{s_{1} + s_{2}}{t_{1} + t_{2}} …… (1)
Also the time t1 is given as:
t_{1} = \frac{distance\ travelled\ while\ walking}{speed\ with\ which\ you\ walks}
t_{1} = \frac{s_{1}}{v_{1}}
The time t2 is given as:
t_{2} = \frac{distance\ travelled\ while\ running}{speed\ with\ which\ you\ runs}
t_{2} = \frac{s_{2}}{v_{2}}
Substitute the value of t1 and t2 in equation (1) to get the average speed as:
236-656_123.JPG
But as can be seen from the given values of and , it can be seen that the distances are equal. Therefore one can equate in the equation above as:
236-649_24.JPG
Substitute the given values of s1 and s2 in the equation above
236-2374_25.JPG
Therefore the average speed is 5.7 ft/s
(b) Given:
Time for which you walk distance, (say s1), t1 = 1.0
Speed with which you walk distance, (say s1), v1 = 4.0 ft /s
Time for which you run distance, (say s2), t2 = 1.0 min
Speed with which you run distance, (say s2), v2 = 10 ft / s
The average speed is given as:
average\ speed = \frac{total\ distance\ travelled}{elapsed\ time}
The total distance you travel is the sum of distance s1 and s2 whereas the elapse time is the sum of time t1 and t2.
Therefore, the average speed of the person is:

average\ speed = \frac{s_{1} + s_{2}}{t_{1} + t_{2}} …… (2)
However the distance s1 and s2 can be given as:
s_{1} = v_{1}t_{1}
s_{2} = v_{2}t_{2}
Substitute the values of and in equation (2) to have
average\ speed = \frac{v_{1}t_{1} + v_{2} t_{2}}{t_{1} + t_{2} }
From the given values, it can be seen that the time t1 and t2 have the same magnitude, therefore we can equate t1 = t2 in the equation above.

236-480_510.JPG
Therefore the average speed in this case is equal to the average of the speed and , which can be calculated by substituting the given values of and as:
236-2069_111.JPG
Therefore the average speed is. 7 ft/s.
Heavenlygoodman
13 Points
7 years ago
You walk 240 m at a speed of 4 ft/s and then run 240 m at a speed of 10 ft/s along a straight track. What is your average velocity in m/s

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