Question

What is the displacement of the object, the object’s average speed, and the object’s average velocity?

A object moves according to the equation `v(t)=4t-t^2`. Sketch an accurate graph of v(t).For the time interval [1, 5] find the distance the object travels, the displacement of the object, the object’s average speed, and the object’s average velocity.

Answer 1

Displacement: 20/3
Average speed = Average velocity = 4/3

Explanation:

So, we know that `v(t) = 4t - t^2`. I'm sure you can draw the graph yourself.

Since velocity is how an object's displacement changes with time, by definition, `v = dx/dt`.

So, `Delta x = int_(t_a)^(t_b) v`, given that `Delta x` is the displacement from time `t = t_a` to `t = t_b`.

So, `Delta x = int_1^5 4t - t^2 = [2t^2 - t^3/3]_1^5 = (2xx5^2-5^3/3) - (2xx1^2 - 1^3/3) = 20/3`.

`20/3` meters? Well, you didn't specify any units.

The average speed is defined as distance divided by time elapsed, and the average velocity is defined as the displacement divided by time elapsed.

Now, we can just take `20/3`, and divide it by the time, so `20/3 -: 4 = 5/3`.

I will assume 1-dimensional motion here, so the distance traveled and the displacement is the same.

Again, units. :P