Question

a horse in a race accelerates at the constant rate of 61 m/s², from rest to a speed of 19.1 m/s. It then maintain that speed and covers another 8.7 m. What is the total time of the race in seconds?

Answer 1

The time of the first part $t_1$ can be found from acceleration definition:

$$a = \dfrac{v_f-v_i}{t_1}$$

where $a = 91m/s^2$ is the acceleration, $v_i = 0$ is the initial speed, and $v_f = 19.1m/s$ is the final speed. Thus, obtain:

$$t_1 = \dfrac{v_f}{a}$$

The time of the second part $t_2$ can be found from the equation of motion with constant speed:

$$t_2 = \dfrac{d}{v_f}$$

where $d = 8.7m$ is the distance.

Finally, the total time is:

$$t = t_1 + t_2\\ t = \dfrac{v_f}{a} + \dfrac{d}{v_f}\\ t = \dfrac{19.1m/s}{61m/s^2} + \dfrac{8.7m}{19.1m/s} \approx 0.77 s$$

Answer. 0.77 s.