Questions: Bill's motorcycle can accelerate at 7.05 m / s^2 at a certain RPM and gear. How far, starting from rest, will Bill travel in the first 2.50 s?

Solution Steps

We are given the following values:

• Acceleration, \( a = 7.05 \, \text{m/s}^2 \)
• Initial velocity, \( u = 0 \, \text{m/s} \) (since Bill starts from rest)
• Time, \( t = 2.50 \, \text{s} \)

To find the distance traveled, we use the equation of motion for uniformly accelerated motion: \[ s = ut + \frac{1}{2} a t^2 \] Since the initial velocity \( u = 0 \), the equation simplifies to: \[ s = \frac{1}{2} a t^2 \]

Substitute the given values into the simplified equation: \[ s = \frac{1}{2} \times 7.05 \, \text{m/s}^2 \times (2.50 \, \text{s})^2 \] \[ s = \frac{1}{2} \times 7.05 \times 6.25 \] \[ s = 3.525 \times 6.25 \] \[ s = 22.03125 \, \text{m} \]

Final Answer