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