Question

Aboy runs along a straight road for the first half distance with a speed v1 and the second half distance with a velocity v,2.what is like mean speed vav for the entire trip?​

Answer 1

V = S / T average speed over distance S

t1 = S/2 / v1 time cover first S/2

t2 = S/2 / v2 time to cover second S/2

T = t1 + t2 total time running

T = S/2 / v1 + S/2 / v2 = S/2 * (1/v1 + 1 / v2)

T = S/2 * (v2 + v1 / (v1 v2)

V = S / {S/2 * (v2 + v1 ) / (v1 v2)

V = 2 * v1 * v2 / [ (v1 + v2)]

Check: suppose t1 = 5 mi / 10 min = 1/2 mi / min

t2 = 5 mi / 20 min = 1/4 mi /min

So runner covers S in 30 min = 10 mi / 30 min = 1/3 mi / min

Our formula says

V = 2 * 1/2 * 1/4 / [(1/2 + 1/4)] = 1/4 / (3 / 4) = 1/3 mi / min