# Relative velocity of two speeding cars

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In summary, the relative velocities of two cars depend on their ground speeds and the direction they are heading in, as well as the chosen frame of reference. When both cars are heading in the same direction, the relative velocity is the difference between their ground speeds. When one car is behind the other, the relative velocity is positive. When the cars are heading towards each other, the relative velocity is the sum of their ground speeds. In this case, the relative velocity is positive when the chosen frame of reference is the car in front, and negative when the chosen frame of reference is the car behind.
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## Homework Statement

Given the following conditions, what is the relative velocity of 2 cars if their ground speeds are 80km/h for Car A and 45 km/h for Car B?
a) both cars are heading in the same direction, A behind B in the reference frame of A
b) Use the reference frame of B for part A)
c) both cars are heading towards each other. take the reference frame of A
d) use B's reference frame for part c.

## Homework Equations

none. i just used simple addition + subtraction.

## The Attempt at a Solution

basically the wording of this problem is really throwing me off. i don't understand what they're trying to ask me to do evne though it seems like an easy question.

im guessing that 35km/h will be the answer for A and B? because i figured if you were sitting in car B, it seems like car A is just going 35 km/h faster..?

The related information from Physics.
Velocity definition: Velocity is speed in a known direction.
Relative Velocity definition: The velocity of an object, A, relative to any other choosen object, B, having velocity, including stationary objects.

General calculation:
Let the velocity of object, A be equated to v1, while the velocity of object, B is equatable to v2. The relative velocity of A with respect to B is written as, Rv(v1,v2), WHEREAS, the relative velocity of B with respect to A is written as, Rv(v2,v1), which is short for Rv(+v1,+v2).

The calculation, Rv(v1,v2) is, Rv(v1,v2) = v1-v2 = (+v1) - (+v2) ;
The resulting value can be positive (+), negative (-), or zero (0).

Because velocity is speed in a known direction, solving physics problems of this nature,
means assigning the directions of travel, in a sane, comprehensive manner. The normal
assignments for direction, starts within the frame of reference, which has been agreed
upon, as positive. Therefore Rv(v1,v2), at least means, that v1 is aligned with a positive
direction. This implies that assignments for direction are done in sequential order, and the
frame of reference is given itz direction, first, before all others.

Any object B, with velocity v2, moving in the same direction, as the direction, the frame
of reference indicates, yields a direction, identical to the frame of reference, (positive)
and the relation written Rv(+v1,+v2) which is identical to Rv(v1,v2).

Any object B, moving in the opposite direction as the direction the frame of reference
indicates, itz directional relationship to the frame of reference is, the opposite,
(negative) and the relation written Rv(+v1,-v2), which is the same as Rv(v1,-v2).

Velocity is a vector (directional) whereas speed is a scalar (non directional).
Here are the steps:
(1) From the given information construct your frame of reference (v1).
(2) Write down the equivalence relation of Rv(v1,v2)
(3) Calculate the relative velocity Rv(v1,v2) = (v1) - (v2), keeping the sign.

Shall we proceed?

solving part a said:
a) both cars are heading in the same direction, A behind B in the reference frame of A
(Step 1)
<---------A (80 km/h) (+)
<----B (45 km/h) (same direction so it is positive (+))
(Step 2) Rv(+80,+45).
(Step 3) Rv(v1,v2) = v1 - v2 = 80km/h - 45km/h = 35km/h
(Step 4) The relative velocity is 35km/h

solving part b said:
b) Use the reference frame of B for part A)
(Step 1)
<----B (45 km/h) (+)
<---------A (80 km/h) (same direction so it is positive)
(Step 2) Rv(+45,+80).
(Step 3) Rv(v1,v2) = v1 - v2 = 45km/h - 80km/h = -35km/h
(Step 4) The relative velocity is -35km/h

solving part c said:
c) both cars are heading towards each other. take the reference frame of A
(Step 1)
<---------A (80 km/h) (+)
B------> (45 km/h) (opposite direction so it is negative)

(Step 2) Rv(+80,-45)
(Step 3) Rv(v1,v2) = v1 - v2 = (+80km/h) - (-45km/h) = 125km/h
(Step 4) The relative velocity is 125km/h.

solving part d said:
d) use B's reference frame for part c.
(Step 1)
<------B (45 km/h) (+)
A---------> (80 km/h) (opposite direction so it is negative)
(Step 2) Rv(+45,+80).
(Step 3) Rv(v1,v2) = v1 - v2 = (+45km/h) - (-80km/h) = 125km/h
(Step 4) The relative velocity is 125km/h.

I would approach this problem by first clarifying the reference frames and the direction of motion for each car. In this scenario, the reference frame is the point of view from which the motion of the cars is observed. The direction of motion is the direction in which the cars are traveling.

a) In the reference frame of car A, car B is moving in the same direction at a slower speed. Therefore, the relative velocity of car B with respect to car A is 35 km/h (80 km/h - 45 km/h).

b) In the reference frame of car B, car A is moving in the opposite direction at a faster speed. Therefore, the relative velocity of car A with respect to car B is 35 km/h (80 km/h + 45 km/h).

c) In the reference frame of car A, both cars are moving towards each other. Therefore, the relative velocity of car B with respect to car A is 125 km/h (80 km/h + 45 km/h).

d) In the reference frame of car B, both cars are moving towards each other. Therefore, the relative velocity of car A with respect to car B is 125 km/h (80 km/h + 45 km/h).

It is important to note that the relative velocity is always calculated with respect to a reference frame and the direction of motion. In this case, the relative velocity changes depending on the chosen reference frame and the direction of motion.

## 1. What is relative velocity?

Relative velocity is the velocity of an object or a system in relation to another object or system. It takes into account the motion of both objects and their respective velocities.

## 2. How is relative velocity calculated?

Relative velocity is calculated by subtracting the velocity of one object from the velocity of the other object. The resulting velocity is the relative velocity between the two objects.

## 3. How does the relative velocity of two cars affect their collision?

The relative velocity of two cars determines the force of impact in a collision. The higher the relative velocity, the greater the force of impact and the more severe the collision will be.

## 4. Can the relative velocity of two cars be negative?

Yes, the relative velocity of two cars can be negative. This indicates that the two cars are moving in opposite directions.

## 5. How does the relative velocity of two cars change if one car changes direction?

If one car changes direction, the relative velocity between the two cars will change. This is because the velocity of the car that changed direction will now have a different direction in relation to the other car, resulting in a change in the relative velocity.

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