What is the speed of the goat at the first point? What is its acceleration?

Question

a goat ran between two points in the plains with a total distance of 85.0m for 10.0 s, with constant acceleration. The speed of the goat when it landed on the final point is 15.0 m/s. What is the speed of the goat at the first point? What is its acceleration?

Answer 1

Let

a (to be computed) be the goat's acceleration,

s(t) be the position of the goat at time t,

v(t) be the speed of the goat at time t.

We are given

s(0) = 0 m,

s(10) = 85 m

v(10) = 15 m/s

We use the following equations, which derive from the definition of acceleration.

v(t) = at + v(0)

s(t) = at²/2 + v(0)t + s(0)

Substituting the given quantities for t = 10

15 = 10a + v(0)

85 = 100a/2 + 10v(0) + 0

Solution to these two equations is

a = 1.3 m/s²

v(0) = 2 m/s