Question

The position of an object at time t is given by s(t) = -8 - 9t. Find the instantaneous velocity at t = 1 by finding the derivative.

Answer 1

Well, in general, the derivative of position is velocity and the derivative of velocity is acceleration. So all it wants you to do is takethe derivative of your function and then plug in t = 1. Well, if you know about derivatives, then you know if you takethe derivative that you simply get -9. Well, there is no t to plug t = 1 into. What this means is that the velocity is constant and is always going to be -9

Answer 2

ok , I understand that, but can velocity be negative?

Answer 3

It can if your displacement is negative :3

Answer 4

Velocity is change in distance over change in time. So a velocity of -9 is like saying that your going backwards -9 units per second.

Answer 5

ooh ok, thank you that was very helpful

Answer 6

Velocity can also be negative if you define directions. For example, in a physics problem you often need to define positive and negative directions. Like if you have a falling object, you may define the downwards direction as positive and upwards, against gravity, as negative. So tossing a ball up into the air, until the ball starts falling back down it will have a negative velocity because of the parameters of the problem that must be defined. So yeah, in a lot of problems you'll definitely have negative velocity and position, etc.

Answer 7

so i guess if north was positive south could be negative, that makes sense.

Answer 8

Yep. Of course for problems like that it's up to you to choose what is positive and negative, but if you always say that velocity must be positive, you'll never get correct answers for a lot of physics problems xD