# Relative motion between cars with different types of movements

• Santilopez10
In summary, the conversation discusses a problem involving the instantaneous acceleration of two cars, A and B, on a circular track. The initial approach involves calculating the angular velocity and acceleration for car A, but the conversation shifts to discussing the relative acceleration between the two cars. The group agrees that it is important to use variables instead of numbers in the calculations for more accurate results. One member points out a sign error in the first equation and the conversation concludes with a final equation for the relative acceleration and a correction to the initial calculation.
Santilopez10
Homework Statement
Car A drives a curve of radius 60m with a constant velocity of 48 km/h. When A is at the given position, car B is at 30m away from the intersection and accelerating at 1.2 m/s^2 to the south. Calculate the lenght and direction of the acceleration that car B would measure of car A from its perspective at that instant.
Relevant Equations
Kinematic equations in polar and cartesian coordinates
I think my approach is quite wrong, still I gave it a shot:
First I know that ##v_A=13.3 m/s=r\omega=60\omega \rightarrow \omega=0.2 \frac{rad}{s}##
Then $$\vec a_A=-r\omega^2 e_r=-2.4 e_r$$
But ##e_r=\cos{\theta}i+\sin{\theta}j## and substituing the latter in the acceleration equation I have that ##\vec a_A= -2i-1.2j##
At last: $$\vec a_{A/B}=\vec a_A - \vec a_B$$
and this is were I stopped, hope you can help me. Thanks!

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Looks to me like you're on the right track. Someone else please correct me if I'm wrong, but this looks like a simple vector addition problem.

Emmo Amaranth said:
Looks to me like you're on the right track. Someone else please correct me if I'm wrong, but this looks like a simple vector addition problem.
I believe it should be wrong because I am not even taking into account the y and x distance that are given to me as information, maybe I should add the relative angular speed of A from B, tbh I am not quite sure.

But should that matter? The question asks for instantaneous acceleration.

not quite sure, that is why I am asking here.

Santilopez10 said:
not quite sure, that is why I am asking here.
If car B were at a different point along the axis, none of the accelerations in the ground frame wouid change, so the relative acceleration cannot change.
But you should resist plugging in numbers straight away. Create variables to replace the given numbers and work symbolically, only plugging in numbers at the end. It has many advantages, one being precision. The answer you got is rather inaccurate.

haruspex said:
If car B were at a different point along the axis, none of the accelerations in the ground frame wouid change, so the relative acceleration cannot change.
But you should resist plugging in numbers straight away. Create variables to replace the given numbers and work symbolically, only plugging in numbers at the end. It has many advantages, one being precision. The answer you got is rather inaccurate.
Okay I ended with $$\vec{a_{A/B}}=(-\frac{v^2}{r}\cos{\theta}+1.2)i-\frac{v^2}{r}\sin{\theta} j$$
Plugging the values I get that $$\vec{a_{A/B}}=-1.36 i -1.5 j \rightarrow |\vec{a_{A/B}}|=2 \frac{m}{s^2} \rightarrow \vec{a_{A/B}}(\theta)=132º$$
Note I changed the axis so that Y points upwards and X points to the right if you were Car B.

Santilopez10 said:
Okay I ended with $$\vec{a_{A/B}}=(-\frac{v^2}{r}\cos{\theta}+1.2)i-\frac{v^2}{r}\sin{\theta} j$$
Plugging the values I get that $$\vec{a_{A/B}}=-1.36 i -1.5 j \rightarrow |\vec{a_{A/B}}|=2 \frac{m}{s^2} \rightarrow \vec{a_{A/B}}(\theta)=132º$$
Note I changed the axis so that Y points upwards and X points to the right if you were Car B.
You have a sign error in the first equation above.

haruspex said:
You have a sign error in the first equation above.
Would you show me where? I am reading this at bed at the moment, it is 00:43 here . If I could afford making the noise to search for my stuff I would do it. (People sleeping here )

Santilopez10 said:
Would you show me where? I am reading this at bed at the moment, it is 00:43 here . If I could afford making the noise to search for my stuff I would do it. (People sleeping here )
Are the two ##\hat i## accelerations in the same sense or opposite sense? Would you expect the relative acceleration to be more or less in magnitude then the max of the two?

Santilopez10
haruspex said:
Are the two ##\hat i## accelerations in the same sense or opposite sense? Would you expect the relative acceleration to be more or less in magnitude then the max of the two?
You are right, it should be -1.2. Thanks a lot for the help!

## 1. What is relative motion between cars with different types of movements?

Relative motion between cars with different types of movements refers to the perceived motion of one car in relation to another car. It takes into account the different speeds, directions, and positions of each car to determine their relative motion.

## 2. How does the relative motion between cars with different types of movements affect collisions?

The relative motion between cars with different types of movements plays a crucial role in determining the outcome of collisions. The impact of a collision is dependent on the relative speeds and directions of the cars involved. For example, a head-on collision between two cars moving in opposite directions at high speeds will have a more severe impact than a rear-end collision between two cars moving in the same direction at lower speeds.

## 3. What is the difference between linear and rotational motion in cars?

Linear motion refers to the movement of a car in a straight line, while rotational motion refers to the movement of a car around an axis or point. In cars, linear motion is associated with the forward and backward movement, while rotational motion is associated with turning or cornering.

## 4. How does the type of road surface affect the relative motion between cars?

The type of road surface can greatly impact the relative motion between cars. A smooth and flat road surface will allow cars to move at a constant speed, while a bumpy or uneven road surface can cause cars to accelerate or decelerate. Similarly, a slippery road surface, such as ice or wet pavement, can significantly affect the relative motion between cars and increase the risk of collisions.

## 5. How do different types of cars, such as sedans and SUVs, have different relative motion?

The size, weight, and aerodynamics of different types of cars can affect their relative motion. For example, SUVs typically have a higher center of gravity and are heavier than sedans, which can make them more prone to tipping and affect their ability to make sharp turns. Additionally, the shape and design of a car can also impact its relative motion, with more aerodynamic cars experiencing less air resistance and thus having a smoother motion.

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