A motorcyclist covers 4 successive 4 km stretches at speeds of 20 kmph, 30 kmph, 40 kmph and 50 kmph respectively. find the average speed over the distance
Answers
A motorcyclist covers 4 successive 4 km stretches at speeds of 20 kmph, 30 kmph, 40 kmph and 50 kmph respectively.
We have to find the average speed over the distance.
To find the average speed over the distance, total time taken by the motorcyclist must be found out.
we know, speed is the rate of change of distance with respect to time.
i.e., speed = distance/time
⇒time = distance/speed
now we can find time for each 4km covered by motorcyclist, can't we ?
with 20 km/h, time taken to cover 4 km , t₁ = 4/20 h
with 30 km/h, time taken to cover 4 km, t₂ = 4/30 h
with 40 km/h, time taken to cover 4 km, t₃ = 4/40 h
with 50 km/h, time taken to cover 4 km, t₄ = 4/50 h
now, average speed = total distance/total time taken
= (4 km + 4 km + 4 km + 4 km)/{4(1/20 h + 1/30 h + 1/40 h + 1/50 h)
= 16/{4(30 + 20 + 15 + 12)/600}
= 4 × 600/77
= 31.17 km/h