Answer to Question #101638 in Physics for ceaser daniel

Question

3. A horse race takes place on a long straight track, at the beginning of the race the horse
accelerates from rest to some top speed with a (constant) acceleration of 1:13 m=s2
3
and then maintains that top speed to the end of the race. The total time taken
from the start of the race to its end is 2:05 minutes and the total distance covered
is 2:41 km.
(a) What was the time elapsed during the acceleration phase of the horse's motion?
(b) What distance did the horse cover during the acceleration phase of its motion?
(c) What was the top speed reached by the horse?

Answer 1

a)

$$d=0.5at^2+v(T-t)=0.5at^2+at(T-t)$$

$$2410=0.5(1.13)t^2+(1.13)t(2.05(60)-t)$$

$$t=18.77\ s$$

b)

$$d=0.5(1.13)(18.77)^2=199\ m$$

c)

$$v=at=(1.13)(18.77)=21.2\frac{m}{s}$$