Question #25118

A racing car accelerates uniformly through 3 gear changes with the following average speeds: 20m/s for 2s,40m/s for 2s,60m/s for 6s.What is the overall average speed?

Expert's answer

V - an overal average speed

S - a total distance

t - a total time

V = S/t

S = V1*t1 + V2*t2 + V3*t3

V1, V2, V3 - average speeds for each gear changes

t = t1 + t2 + t3

t1, t2, t3 - times for each gear changes

Finally:

V = (V1*t1 + V2*t2 + V3*t3)/( t1 + t2 + t3) = (20*2+40*2+60*6)/(2+2+6)=48 m/s

Answer: the overall average speed equals 48 m/s

S - a total distance

t - a total time

V = S/t

S = V1*t1 + V2*t2 + V3*t3

V1, V2, V3 - average speeds for each gear changes

t = t1 + t2 + t3

t1, t2, t3 - times for each gear changes

Finally:

V = (V1*t1 + V2*t2 + V3*t3)/( t1 + t2 + t3) = (20*2+40*2+60*6)/(2+2+6)=48 m/s

Answer: the overall average speed equals 48 m/s

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