Question

Olympic swimmer Michael Phelps swam at an average speed of 2.01m/s during the first half of the time needed to complete a race. What is his average swimming speed during the second half of the race if he tied the record which was at an average speed of 2.05m/s?

Answer 1

Here average speed for given motion is defined as ratio of total distance covered by total time

so here we can say

$v = \frac{d}{t}$

here total distance can be calculated by formula

distance = speed * time

$v = \frac{v_1*t_1 + v_2*t_2}{t_1 + t_2}$

here given that its average speed is v = 2.05 m/s

for first half let the time is "t " seconds and the speed for that is 2.01 m/s

and for next half time will be same and it is "t " seconds again

so by plug in all data in above equation we have

$2.05 = \frac{2.01* t + v* t}{t + t}$

$2.05 * 2 = 2.01 + v$

$v = 2.09 m/s$

so its speed for next half must be 2.09 m/s