Final answer:
The average velocity of a body covering equal halves of a journey at different velocities is calculated using the harmonic mean, giving approximately 44.44 m/s, which is rounded to 44 m/s. Hence, option (a) is the correct answer.
Step-by-step explanation:
To find the average velocity of a body that covers one-half of its journey at 40 m per second and the next half at 50 m per second, we need to consider the harmonic mean of the velocities because the distances are equal. The average velocity (Š) can be calculated using the formula for the harmonic mean of two velocities, Š = 2/(1/v1 + 1/v2), where v1 and v2 are the two velocities.
Substituting the given velocities into the formula we get:
Š = 2 / (1/40 m/s + 1/50 m/s) = 2 / (50 + 40)/(40 × 50) m/s
Š = 2 / (90/2000) m/s
Š = 2 × 2000/90 m/s
Š = 4000/90 m/s
Š = 44.44 m/s
Therefore, the average velocity is approximately 44.44 m/s, which would be rounded to 44 m/s when considering the given options.