Question

The position of an object any this given by s(t)=2t^2 -8t+10 a. Determine the velocity of the object? b. Is the object moving to the right or left at t=1? c.is the object right or left at t=4?

Answer 1

I tried this:

Explanation:

Let us plot our position function:

graph{2x^2-8x+10 [-10, 10, -5, 5]}

We can see that at `t=1` the object is at `s=4m` and increasing the time the position of the object will decresae (move to the left) it stops at `t=2` and then starts to move towards the right increasing its distance from point at `s=2m`.

I would derive your position function to find the velocity::

`v(t)=(ds)/(dt)=4t-8`

at `t=1` we get

`v(1)=(4*1)-8=-4m/s`

the minus sign tells us that the velocity is towards the left (having choosen the positive `x` direction as right).

at `t=4` we get:

`v(4)=(4*4)-8=16-8=8m/s`

this time the positive value of the velocity tells us that it is twards the right.