# Instantaneous velocity and friction

1. Mar 21, 2004

### pineapple629

We need to know the instentaneous velocity formula for a car launched down a hallway. we also need to figure out how to calculate all the friction involved in this. please help.

2. Mar 21, 2004

### Chen

The car's velocity at a certain moment $$t$$ is:
$$\vec V(t) = \vec V_0 + \vec at$$
The car's acceleration is defined as:
$$\vec a = \frac{\vec \Sigma F}{m}$$
In this case the only force on the motion axis (X) is the friction:
$$\vec a = \frac{\vec f_k}{m} = \frac{-N\mu }{m} = \frac{-mg\mu }{m} = g\mu$$

Therefore the car's velocity is:
$$\vec V(t) = \vec V_0 - g\mu t$$