If a particle's position is given by x=4-12t+3t^2, where t is in seconds and x is in meters, what is its velocity at t=1 second?

v = - 5 m/s

Explanation:

The position is given by:

x = 4 - 12t + 3t²

Then, we need to know the position of the particle at 1 second.

So we evaluate the equation using this time.

X (1) = 4 - 12 (1) + 3 (1) ²

X (1) = 4 - 12 + 3

X (1) = - 5 m

But velocity equals position/time

So: velocity = - 5m / 1 s

velocity = - 5 m/s