Question

a cyclist cycles for t sec at a speed of 3m/s and then for the same time at a speed of 5m/s along a straight road due north. what is the average speed of the cyclist

Answer 1

average velocity = total distance travelled / time taken
so, we have to calculate the total distance travelled by the cyclist.
thus, the distance travelled by the cyclist in the first t secs
s = 3xt
similarly, the distance travelled by the cyclist in last t secs
s = 5xt
so, total distance travelled
s = s + s = 3t + 5t = 8t
total time taken = t + t = 2t
so, average velocity will be
v = 8t/2t
or
v = 4 m/s

Answer 2

the answer for your question is