A boy is running on a straight road.He runs 500m towards north in 2minutes 10seconds and then turns back and runs 200m in 1.00 minute.Calculate his average speed and magnitude of average velocity during first 2minutes 10seconds and his average speed and magnitude of average velocity during the whole journey.
Answers
Given that, a boy is running on a straight road. He runs 500 m towards the north in 2 min 10 sec.
Let us assume that the boy starts from point A to point B and travels 500 m towards the north.
Means, distance covered by him from pint A to point B is 500 m in 2 min 10 sec.
Here, distance = 500 m and time = 2min 10 sec = 2*60 + 10 = 130sec
Average speed = Distance/Time
= 500/130
= 3.8 m/s
Displacement is also the same i.e. 3.8 m/s.
Also given that, later he turns back and runs 200 m in 1 min.
From point B to point C, distance travelled by boy is 200 m in 1 min or 60 sec.
Now,
Distance = 200 m and time = 1min = 60 sec
Average speed = 200/60
= 3.33 m/s
The total average speed of the boy in the whole journey = (3.8 + 3.3)/2 = 7.1/2 = 3.5 m/s
Now,
{ Displacement = 500 - 200 = 300 m
Time = 130 - 60 = 70 sec }
The total average velocity of the boy in the whole journey = 300/70 = 4.2 m/s.
Given :-
A boy is running on a straight road. He runs 500 m towards north in 2 minutes 10 seconds and then turns back and runs 200 m in 1 minute.
To find :-
• The average speed and magnitude of average velocity during first 2 minutes 10 seconds.
• The magnitude of average velocity during the whole journey.
Solution :-
Let the boy start from a point A and B point is 500 m away from it. Let C be 200 m far from B.
Total time taken to reach B from A = 2 mins 10 secs
= 120 secs + 10 secs
= 130 secs
Distance travelled = Displacement = 500 m
Speed = Distance/Time
⇒Speed = 500/130
⇒Speed = 3.84 m/s
In this case, speed = velocity = 3.84 m/s (As distance = Displacement)
A/q, he turns back and runs 200 m in 1 min later.
Or, from B to C, the boy travels 200 m in 60 s.
So, avg. speed = distance/time
⇒Avg. speed = 200/60
⇒Speed = 3.33 m/s
Total average speed of the boy = (3.84 + 3.33)/2 = 7.17/2 = 3.58 m/s
Now, displacement from A to C = 500 - 200 = 300 m
And time taken from reaching A to C = 130 - 60 sec = 70 sec
So, average velocity = Displacement/time
⇒Avg. velocity = 300/70