A particle's position (in meters) is given by the equation s(t) = 5x sin(2x), on the interval [-1, 4] minutes. What is its instantaneous velocity at t=0

Question

It should be 0 right because t = 0?

Answer 1

Y=5xsin(2x),.

The derivative is the velocity function.

Y'= 5(sin(2x)+2xcos(2x) )

Evaluate at t =0 , 5(0+0) =0 equals the instantaneous velocity at t =0.

Answer 2

Not necessarily! t=0 just refers to the point at which we begin measuring - it is perfectly reasonable to think that the particle may be already moving. For instantaneous velocity at a given time, we do the following:

1. Make sure the given point is within the given interval (yes in this case)
2. Take the derivative of the position function - the derivative of position is velocity.
3. Substitute t=0 into the velocity function.

This may very well turn out to be 0, but it is not something we can assume.