# Instanteneous velocity question

1. Apr 5, 2005

### jhson114

two cars A and B are traveling in a straight line. Car A is passing car B and at time t1, car A is adjacent to car B. If each cars are travelling in a constant speed ( each with seperate constant speed), at time t1, instanteneous velocity of car A should be greater than car B right?? since in order for car A to pass car B, velocity of car A has to be greater than car B, and since their velocity is constant throughout motion, car A should have greater instanteneous velocity at t1.
also, it shouldnt matter if car B is accelerating and car A is travelling in a constant velocity.. right? since even though B is accelerating car A must have greater velocity at t1 in order to pass car B, therefore instanteneous of car A should still be greater. please correct me if i'm wrong. thank you

2. Apr 5, 2005

### whozum

Correct. Car A cant pass Car B if they both have constant velocities and car B has a higher one.
Car A cant pass Car B unless its velocity at the time of passing is greater, correct. However, theres no say as to what may happen later on:

The position equation for Car A and Car B are as follows:

$$x(t)_a = v_0t$$

$$x(t)_b = v_{0b} + \frac{at^2}{2}$$

It is very possible that the initial velocity of car B will be lower than Car A, at which point t=t1 car A will pass, but as t increases, the acceleration will eventually cause car B to pass car A again.

3. Apr 5, 2005

### codyg1985

If each car is travelling at a constant speed as you say, then neither car is accelerating, which means that once car A passes car B, car B will not overtake car A again.

4. Apr 5, 2005

### HallsofIvy

Staff Emeritus
In fact, if both cars are traveling at constant speed, there is no need to talk about "instantaneous" velocity- instantaneious= average= constant speed will do nicely.

If B is accelerating, then you do need to say "instantaneous". Of course, knowing only the acceleration tells you nothing about the speed at a giving instant.