Questions: If a racehorse starts from rest and accelerates at a rate of 4.7 m / s^2, how long does it take the horse to go 20 m? A. 9.1 s B. 4.3 s C. 8.5 s D. 2.9 s

Solution Steps

We are given:

• Initial velocity, $u = 0 \, \text{m/s}$ (since the horse starts from rest)
• Acceleration, $a = 4.7 \, \text{m/s}^2$
• Distance, $s = 20 \, \text{m}$

We need to find the time $t$. The kinematic equation that relates distance, initial velocity, acceleration, and time is: $$s = ut + \frac{1}{2}at^2$$

Substitute the known values into the equation: $$20 = 0 \cdot t + \frac{1}{2} \cdot 4.7 \cdot t^2$$ $$20 = 2.35 t^2$$

Rearrange the equation to solve for $t$: $$t^2 = \frac{20}{2.35}$$ $$t^2 \approx 8.5106$$ $$t \approx \sqrt{8.5106}$$ $$t \approx 2.9182 \, \text{s}$$

Final Answer