Ratio of Space-Average Velocity to Time Average Velocity
Understanding the Concept of Space-Average Velocity and Time Average Velocity:
- Space-average velocity is the average velocity of a particle over a given distance or space. It is calculated by dividing the total displacement by the total time taken.
- Time average velocity is the average velocity of a particle over a given time interval. It is calculated by dividing the total displacement by the total time taken.
Calculating the Ratios:
- Let the initial velocity of the particle be u, acceleration be a, final velocity be v, and time taken to reach final velocity be t.
- The space-average velocity (v_avg) can be calculated using the formula: v_avg = (u + v) / 2
- The time average velocity (v_tavg) can be calculated using the formula: v_tavg = total displacement / total time taken
- The total displacement can be calculated using the formula: s = ut + (1/2)at^2
- The total time taken can be calculated using the formula: t = v / a
- Substituting the values and calculating, we get v_avg = v_tavg
Therefore, the ratio of space-average velocity to time average velocity is 1:1. This means that in the given scenario of a particle starting from rest with constant acceleration, the space-average velocity is equal to the time average velocity.