Question

position for an object given s(t)=2t^2-6t-4, what is the total distance travelled on [1,4]

Answer 1

The object's position at t = 1 is:
\[2(1)^2 - 6(1) -4 =-8\]
The object's position at t = 4 is
\[2(4)^2 - 6(4) - 4 = 4\]

Answer 2

The difference between the initial and final positions is:
\[x_f - x_i = 4 - (-8) = 12\]

Answer 3

Interestingly, though, if you put a pedometer on the object, that would not be what it measures.

Answer 4

The object's motion is given by:
\[s = 2t^2 - 6t - 4\]
This is a parabola, which has a vertex at
\[t =3/2\]
which means that the object actually turns around at t = 3/2

Answer 5

A pedometer on the object would measure the sum of the distance traveled between the intervals [1,3/2] and [3/2, 4].

Answer 6

The object's position at t = 3/2 is:
\[ 2(1.5)^2 - 6(1.5) - 4 = -8.5\]

Answer 7

So, between 1 and 3/2, the object travels .5, and between 3/2 and 4 it travels 12.5

Answer 8

A pedometer placed on this object would measure that the object traveled 13 units

Answer 9

I don't know which answer the question wants, 12 or 13. It is probably 12, but I am not sure.

Answer 10

Rhanks so much!

Answer 11

You are welcome