easy velocity question?

Question

If you know the posistions of a particle at two points along its path and also know the time it took to get from one point to the other, can you determine the particles instataneous velocity? its average velocity? Explain.

Answer 1

The instantaneous velocity is given by the rate of the change in the particle's position. If the position is given by the vector R = (Rx, Ry, Rz), then we can write the change in position by delta R = (R2x - R1x, R2y - R1y, R2z - R1z) where 1 and 2 are starting and final positions. You would then divide these values by the time to get the AVERAGE velocity, which is expressed as V = (Vx, Vy, Vz) where for example Vx = (R2x - R1x)/t.

Based on the information given, however, you would not be able to find the instantaneous velocity unless you knew an equation for the particle's position or acceleration relative to time. Instantaneous velocity is like reading off the spedometer of your car at any one particular moment whereas average velocity takes into account a change over a long time. Usually to find instantaneous, it is the limit of average velocity, as the time interval gets smaller and smaller.

Answer 2

average velocity? Yes. average velocity is
Change in position / elapsed time

instataneous velocity? No. The particle's velocity could be changing in many ways as it goes from one point to the other. instataneous velocity is
Change in position / an infinitesimal time

instataneous velocity is the reading on a speedometer at any moment.

average velocity on the trip to school is the distance to school/time it took to get there, including stopping at the coffee shop.

Answer 3

Use v = u + at, the position v is the perfect speed, u the preliminary speed, and t the time taken. because the ball is falling less than gravity, g is +ve g is basically -ve at the same time as an merchandise is thrown upwards, because it really is then decelalerating. v =u + at v = 0 + 9.8 x 3 v = 29.4 m/sec.