# A car catching up to another car

• Whitishcube
In summary, the problem involves two cars, one moving at 95 km/hr and the other at 75 km/hr. The question is how long it would take for the faster car to catch up to the slower car. Using kinematic equations, the change in time can be found by setting the final position of the slower car to the initial position of the faster car, and then solving for the change in time. The result is 19.8 seconds.
Whitishcube

## Homework Statement

a car moving 95 km/hr is 110 meters behind another car going 75 km/hr. how long does it take for the faster car to catch up?

## Homework Equations

kinematic equations

## The Attempt at a Solution

so i manipulated the kinematic equations to yield an expression for the change in time, but my problem is finding which is initial velocity and which is final. do i have to consider the motion of both cars SEPARATELY? or maybe take the difference of the two velocities and use that as the velocity for the change in distance? any help here would be greatly appreciated. (i also note that the velocities must be converted to m/sec.)

actually i think i might have gotten it. i used the equation

final position = initial position + (init. velocity)(change in time) + (0.5)(accel)(change in time)^2

for both cars, setting acceleration to zero for both.
for the car i set its initial position as zero and final as 110 meters. then for the truck i set BOTH finial and initial position to 110. from there i set the two equations equal to each other and solved for change in time. my final answer is 19.798 seconds. is this the right way to go about this problem?

All you have to do is count how long would it take if both cars were by 75km/h slower. So use this in the equation v=s/t...t=s/v.
The result I got was exactly 19.8, so I'm not sure where you got the -0.002. If it's from conversion of speeds to m/s, I think it's easier just to consider the distance as km (110m=0.11km), get the result in hours and multiply by 3600 to get it in seconds.

## 1. How does a car catch up to another car?

There are a few factors that contribute to a car catching up to another car. Firstly, the speed and acceleration of the cars play a major role. If one car has a higher speed and/or acceleration, it will be able to catch up to the other car. Secondly, the distance between the two cars is important. If the cars are relatively close together, the faster car will be able to catch up more quickly.

## 2. Can a slower car catch up to a faster car?

Yes, it is possible for a slower car to catch up to a faster car. This could happen if the faster car has to slow down due to traffic or other obstacles, while the slower car maintains a steady speed. Additionally, if the slower car has a higher acceleration, it may be able to catch up to the faster car.

## 3. What is the role of aerodynamics in a car catching up to another car?

Aerodynamics can play a significant role in a car catching up to another car. A car with better aerodynamics will experience less air resistance, allowing it to maintain higher speeds and accelerate more quickly. This can give it an advantage in catching up to a slower car with less efficient aerodynamics.

## 4. How long does it take for a car to catch up to another car?

The time it takes for a car to catch up to another car can vary greatly depending on the speed and acceleration of the cars, as well as the distance between them. In ideal conditions, a car with a higher speed and acceleration could catch up in a matter of seconds. However, in real-world situations, factors such as traffic and road conditions can affect the time it takes for a car to catch up.

## 5. Can two cars ever have the same speed and not catch up to each other?

Yes, it is possible for two cars to have the same speed and not catch up to each other. This could happen if both cars are traveling at a constant speed and neither car has a higher acceleration. In this case, the distance between the cars would remain the same, and they would not catch up to each other.

Replies
1
Views
1K
Replies
11
Views
953
Replies
4
Views
1K
Replies
33
Views
4K
Replies
11
Views
2K
Replies
4
Views
2K
Replies
2
Views
3K
Replies
7
Views
1K
Replies
2
Views
2K
Replies
12
Views
2K