Physics 311, Quiz #4

An electron moves so that its position as a function of time (in seconds) is given by

   vector  r(t) =  (5 m) i  -  (3 m/s)*t j  +  (1 m/s^2)*t^2 k

Here the letters i and j represent the unit vectors, usually written in boldface or with a pointy hat accent over them.

Question 1: What is the electron's instantaneous velocity at time t = 3?

                dr
      v(t)  =  ----  =  (0 m/s) i  -  (3 m/s) j  +  (2 m/s)*t k
                dt

      At t = 3 s, 

                     =  (0 m/s) i  -  (3 m/s) j  +  (6 m/s) k

Question 2: What is the electron's average acceleration between t = 3 s and t = 6 s?

                dv
      a(t)  =  ----  =  (0 m/s) i  +  (0 m/s) j  +  (2 m/s) k
                dt

      This acceleration is constant -- it does not change with time.
		Thus, the average acceleration between t = 3 and t = 6 is
		the same as the acceleration at t = 3 or t = 6, or any other
		time:

                     =  (0 m/s) i  +  (0 m/s) j  +  (2 m/s) k

Question 3: What is the electron's instantaneous acceleration at t = 6 s?

                dv
      a(t)  =  ----  =  (0 m/s) i  +  (0 m/s) j  +  (2 m/s) k
                dt

      Again, the acceleration is constant, so it has this value
		at t = 6 seconds.

This page maintained by Michael Richmond. Last modified Dec 17, 2001.