To find the velocity \( v \) and acceleration \( a \) given the time period \( T \) and distance \( d \), we can use the following definitions:
Velocity (average) is calculated by the formula: \[ v = \frac{d}{T} \] where:
- \( d = 0.06 \, \text{m} \) (distance)
- \( T = 0.024 \, \text{s} \) (time)
Plugging in the values: \[ v = \frac{0.06}{0.024} \approx 2.5 \, \text{m/s} \]
Acceleration requires more information about the change in velocity over time. If we assume constant acceleration, we would need the initial and final velocities to calculate it. However, if the object moves a distance \( d \) with constant acceleration \( a \) over time \( T \), we use the formula: \[ d = v_0 T + \frac{1}{2} a T^2 \] assuming \( v_0 = 0 \) (initial velocity is zero): \[ d = \frac{1}{2} a T^2 \] Rearranging gives: \[ a = \frac{2d}{T^2} \]
Plugging in the known values: \[ a = \frac{2 \times 0.06}{(0.024)^2} \approx \frac{0.12}{0.000576} \approx 208.33 \, \text{m/s}^2 \]
So the results are:
- Velocity \( v \approx 2.5 \, \text{m/s} \)
- Acceleration \( a \approx 208.33 \, \text{m/s}^2 \) (assuming initial velocity is zero).
