Joseph jogs from one end A to the other end B of a straight 300 m road in 2 minutes 50 seconds and then turns around and jogs 100 m back to point C in another 1 minute. What are Joseph’s average speeds and velocities in jogging (a) from A to B and (b) from A to C?
Answers
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a) Given,
Total distance from A to B = 300 m
Total time taken from A to B = 2 minutes 30 seconds
= 2 × 60 + 30
= 120 + 30
= 150 s
Average speed (from A to B) === 2.0 m/s (i)
The displacement and the time were taken of Joseph is the same in going from A to B i.e., 300m and 170 s respectively.
Therefore, Average velocity (from A to B) == = 2.0 m/s (ii)
So, from (i) and (ii) it is clear that the average speed and average velocity of Joseph during his jogging are the same.
(b) Given,
Total distance from A to C = 300 + 100= 400 m
Total time = 2 minutes 30 seconds + 1 minutes
= 150 s + 60 s (As we Know 1 Minute= 60 seconds)
= 210 s
Average Speed (from A to C) = = = 1.90 m/s (iii)
Now the average velocity of Joseph from A to C:
Displacement = 300 – 100= 200 m
Total time taken is the same as that of the time taken from A to C i.e., 210 s (Calculated Above)
Average velocity (from A to C) =
From (iii) and (iv) it is clear that the average speed of Joseph is different from his average velocity.
Solution :
The given situation can be shown diagrammatically as follows:
(a) From A to B, distance covered by Joseph = 300 m
Time taken by Joseph for going from A to B
= 2 minutes 50 seconds
= 170 s
NOw, average speed for going from A to B
= tOtal distance travelled/Total time taken
= 300m/170s
= 1.76 ms^-1
Here, total displacement from A to B = Distance between A to B = 300 m
So, the average velocity for going from A to B
= Total displacement/Total time taken
= 300m/170s
= 1.76 ms^-1
(b) From A to C, the distance covered by Joseph
= Distance from A to B +Distance from B to C.
= 300 m + 100 m = 400 m
Time taken by Joseph for going from A to C
= Time taken to move from A to B + Time taken to move from B to C
= 2 minutes 50 seconds + 1 minute
= 170 s + 60 s
= 230 s
Now, average speed tor going from A to C
= Total distance travelled/Total time taken
= 400m/230s
= 1.739 ms^-1
Here, total displacement from A to B
= Displacement from A to B - Displacement from B to C
= 300 m - 100 m
= 200m
Thus, the average velocity for going from A to C
= Total displacement/total time taken
= 200 m/230 s
= 0.869 ms^-1
