Question

You collect some data on horse racing along a straight track. You are able to fit the motion of the horse to a function during this interval, where you’ve chosen a particular spot on the track to be your origin and started your clock (t = 0) when you started collecting this new data.Required:a. What is the horse’s velocity as a function of time? Does the horse ever turn around during this time?b. What is its acceleration as a function of time?

Answer 1

The equation is missing in the question. The equation is
`$10 m + 5(m/s^2)t^2+3(m/s^3)t^3$`

a).
`$v=10 t +9t^2$` , the horse will not turn.

b). a(t) = 10 + 18t

Step-by-step explanation:

Given :

`$x(t)=10 m + 5(m/s^2)t^2+3(m/s^3)t^3$`

∴ At t =0, x = 10 m

a). Velocity as a function of time

`$v = (dx)/(dt) $`

=
`$10 t +9t^2$`

Turning velocity must be zero.

v(t) = 0

`$10 t +9t^2=0$`

`$\therefore t = 0 \text{ or}\ t =-(10)/(9)$`

Taking the positive value of time.

The horse will not turn.

b). Acceleration as a function of time.

`$a(t)=(dv)/(dt)$`

= 10 + 18t

∴ a(t) = 10 + 18t