Speed and Velocity
Speed:
- Total distance covered by a body divided by time taken by it is called speed.
- Speed = Distance / Time taken
- SI Unit of speed is meter/second (m/s).
- Speed is a scalar quantity.
Table of Contents
Instantaneous speed:
- The speed of a body at a particular moment is called instantaneous speed. The instantaneous speed of a body is equal to the speed of that body at that moment in which we are observing it.
- Speedometer of a vehicle measures instantaneous speed and Odometer is used to measure total distance travelled by body.
Average speed:
- The average speed of a body is equal to the total distance travelled by the body divided by the total time taken by it on its entire journey.
- Average speed = Total distance travelled / Total time taken , this formula is true in all conditions and have no limit.
- Average speed = (speed 1 + speed 2) / 2 = (v1 + v2) / 2 , But this formula is applicable only when the body moves for the same time (t) with velocity v1 and v2.
Velocity:
- Total displacement covered by body divided by time taken by it called velocity.
- Velocity = Displacement / Time taken
- Velocity = (final position – initial position) / time taken
- SI Unit of velocity is meter/second (m/s)
- Velocity is a vector quantity.
Relative Velocity:
Velocity of a body with respect to another body is called relative velocity.
Example 1:
A man goes from Agra to Delhi, a distance of 250 km by bus in 5 hours. He stayed there an hour for shopping and came back by train in 4 hours. Calculate the speed of man for the entire journey.
Ans: Total distance travelled by man = 250km + 250km = 500km
Total time taken = 5 + 1 + 4 = 10hour
Average speed = Total distance travelled / Total time taken = 500km / 10hour = 50km/h
Example 2:
A tourist residing in Agra wants to visit Sariska National Park, Rajasthan, located at a distance of 180 km from Agra. He started his car at 6:00 a.m. and reached the national park at 9:00 a.m. For some reason, the national park was closed that day. He returns immediately and reaches Agra at 1:00 pm. Calculate the speed of the tourist’s forward and reverse journey. Also compute the speed of the entire journey.
Ans: Speed of tourist in forward journey (Agra to Rajasthan) = Distance travelled / Time taken = 180 / 3 = 60km/h
Speed of tourist in reverse journey (Agra to Rajasthan) = Distance travelled / Time taken = 180 / 4 = 45km/h
Speed of tourist in entire journey = Total distance travelled / Total time taken = (180 + 180) / 7 = 360/7 = 51.42km/h
👉❌ We can not calculate speed using formula vav = (v1 + v2) / 2 = (60 + 45) / 2 = 52.5km/h ❌ as journey time is not same for the both speed.
Example 3:
A motorcyclist drives from A to B with a uniform speed of 30 km/h and returns back with a speed of 20km/h. Find its average speed.
Ans: From A to B
Distance = X
Speed of motorcyclist 30 km/h
Time taken by motorcyclist t1 = distance / speed = X / 30
From B to A
Distance = X
Speed of motorcyclist 20 km/h
Time taken by motorcyclist t2 = distance / speed = X / 20
Average speed of motorcyclist for entire journey (from A to B and B to A) = total distance / Time taken
= ( X + X ) / t1 + t2 = 2X / ( X / 30 + X / 20 ) = 24km/h
Note: In above problem you can not use formula Average speed = ( V1 + V2 ) / 2 Because time is different for both journey. If a body moves with different velocity V1 and V2for same interval of time t and t then only we can use formula Average speed = ( V1 + V2 ) / 2
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