Example: determining the average velocity, average speed and the acceleration of a particle

A particle moves along a straight line such that its position is defined by s(t) = t^2 -6t + 5. Determine the average velocity, the average speed, and the acceleration of the particle when t = 6. To learn more about particle dynamics, go to https://www.udemy.com/course/mechanic....

The difference between velocity and speed is that velocity is a vector, and speed is a scalar. For finding the average velocity, we take the position where the particle starts, at t= 0, and the position at t = 6, and divide the displacement by time to get average velocity. The equation for position is s = t^2 - 6t + 5. At t = 0 , the particle is at 5m. For t = 6, the particle is again at 5m, so the average velocity is zero.

The average speed, however, is different. This is the total distance travelled divided by time. We need to take the path that the particle travelled, into account. This is carefully explained in the video.

For the acceleration we are looking for the instantaneous acceleration at t = 6. Acceleration = dv/dt. We take the second time derivative of the position, and substitute to get the acceleration. See the explanation in the video.