Question

An electron moves in the positive \(x\) -direction a distance of \(2.42 \mathrm{~m}\) in \(2.91 \cdot 10^{-8} \mathrm{~s}\), bounces off a moving proton, and then moves in the opposite direction a distance of \(1.69 \mathrm{~m}\) in \(3.43 \cdot 10^{-8} \mathrm{~s}\). a) What is the average velocity of the electron over the entire time interval? b) What is the average speed of the electron over the entire time interval?

Short answer

Solution: a) Average velocity = Total displacement / Total time interval = 0.73m / (6.34 * 10^{-8} s) b) Average speed = Total distance / Total time interval = 4.11m / (6.34 * 10^{-8} s)

Step-by-step solution

a) Calculating average velocity.

To find the average velocity, we need to find the total displacement and divide it by the total time interval. The total displacement is the resultant distance in a particular direction, which is the difference between the distances in the positive and negative x-directions (2.42m - 1.69m). The total time interval is the sum of the time intervals in both directions. Total displacement = 2.42m - 1.69m = 0.73m Total time interval = 2.91 * 10^{-8} s + 3.43 * 10^{-8} s = 6.34 * 10^{-8} s Average velocity = Total displacement / Total time interval = 0.73m / (6.34 * 10^{-8} s)

b) Calculating average speed.

To find the average speed, we need to find the total distance covered and divide it by the total time interval. The total distance is the sum of the distances in both directions. Total distance = 2.42m + 1.69m = 4.11m Total time interval = 2.91 * 10^{-8} s + 3.43 * 10^{-8} s = 6.34 * 10^{-8} s Average speed = Total distance / Total time interval = 4.11m / (6.34 * 10^{-8} s)