Question

This should be pretty easy. However, I thought both questions meant the same thing. Apparently not.

Problem: A particle's position is given by x = 8.00 - 12.00t + 3t^2, in which x is in meters and t is in seconds. (a) What is its velocity at t = 1 s? (b) What is its speed just then?

Answer 1

take the derivative and replace \(t\) by \(1\)

Answer 2

And I get -6

Answer 3

ok

Answer 4

then the velocity is \(-6\) and the speed is \(|-6|=6\)

Answer 5

why does the speed have an absolute value and the velocity doesn't. That's what I'm not getting

Answer 6

speed is positive

Answer 7

for example, if you get in your car, put it in reverse, and drive at 10 mph in reverse, your speed is 10 mph but your velocity is -10 since you are going backwards

Answer 8

or as a less silly example, if a rock is falling at a rate of 6 meters per second, then the speed is 6 meters per second, but the velocity is -6 because it is going down, not up

Answer 9

ah ok

Answer 10

Thank you!!!

Answer 11

yw