# 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.
```