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.

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This page maintained by Michael Richmond.
Last modified Dec 17, 2001.
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Copyright © Michael Richmond. This work is licensed under a Creative Commons License.