A horse starts from rest and speeds up with constant acceleration. If it has gone a distance of 100 m at the point when it reaches a speed of 12 m/s, what is its acceleration?

Answer 1

Hi Olivia!

Given that the horse has a constant acceleration, we can use the kinematic equation:

V² = V₀² + 2·a·Δx

where V is the velocity after the horse has traveled a distance of Δx at a constant velocity of a starting from an initial speed, V₀. The goal is to solve for the acceleration, so we can rearrange the kinematic equation by first subtracting V₀² to the left side:

V² - V₀² = 2·a·Δx

Then we can divide both sides by 2·Δx:

(V² - V₀²)/(2·Δx) = a

Based on the problem, the horse starts at rest, so V₀ = 0. The horse travels 100 m, so Δx = 100 m, and the horse reaches a speed of 12 m/s, so V = 12 m/s. Plugging in these values into the equation above:

a = ((12 m/s)² - 0²)/(2·(100 m)) = (144 m²/s²)/(200 m) = 0.72 m/s²

I hope this helps!

Seth