Kinematics in 1 dimension - 2 objects interlinked, find time

In summary, a race driver makes a pit stop to refuel and leaves the pit area with an acceleration of 5.5 m/s^2. After 4.1 seconds, he enters the main speedway where another car traveling at a constant velocity of 69.4 m/s overtakes and passes him. The entering car maintains its acceleration. The question is asking how long it will take for the entering car to catch up with the other car. In order to solve this problem, you will need to use equations from kinematics, specifically the equations for displacement and velocity. Drawing a graph or diagram can help you visualize the situation and determine which equations to use.
  • #1
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A race driver has made a pit stop to refuel. After refueling, he starts from rest and leaves the pit area with an acceleration whose magnitude is 5.5 m/s^2; after 4.1 seconds he enters the main speedway. At the same instant, another car on the speedway and traveling at a constant velocity of 69.4 m/s overtakes and passes the entering car. The entering car maintains its acceleration. How much time is required for the entering car to catch up with the other car?

Homework Equations


I DO NOT understand how do those type of questions. I had a lot of difficulty with this question and could not come up with the right answer. Along with helping me with this question, are there any specific strategies to go about solving these type of questions??

The Attempt at a Solution


After refueling, car #1
Vi= 0m/s
a= 5.5 m/s^2
t= 4.1 s
vf= ? Vf= vi + at
Vf = 0 + (5.5)(4.1)
vf = 22.55 m/s

____
Other car, car #2
V= 69.4 m/s
t= 4.1 s

deltax = vt + 1/2at^2
deltax = (69.4)(4.1) + 0
deltax = 284.54 m

and from here... I'm completely stuck.
Help, please!
 
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  • #2
It helps to draw a diagram or graph of what is going on. I would recommend a graph showing x vs t of both vehicles for starters.
 

Related to Kinematics in 1 dimension - 2 objects interlinked, find time

1. How do I determine the time it takes for two objects to reach a specific distance when they are interlinked?

To determine the time for two interlinked objects to reach a specific distance, you will need to use the formula d = d0 + v0t + 1/2at2 where d is the final distance, d0 is the initial distance, v0 is the initial velocity, a is the acceleration, and t is the time. You will also need to use the equation v = v0 + at to solve for the initial velocity at a specific time. Once you have these values, you can plug them into the first equation and solve for t.

2. What are the units for time in kinematics equations?

The units for time in kinematics equations are typically measured in seconds (s). However, depending on the specific equation being used, time may also be measured in milliseconds (ms), minutes (min), or hours (h). It is important to pay attention to the units and use conversions if necessary to ensure accurate calculations.

3. Can one object affect the time it takes for another object to reach a certain distance?

Yes, one object can affect the time it takes for another object to reach a certain distance if they are interlinked. This is because the acceleration of one object can impact the velocity of the other object, which in turn affects the time it takes to reach a specific distance. This is especially true in scenarios where the objects are connected and moving together, such as in a pulley system.

4. How does the mass of the objects affect the time it takes for them to reach a specific distance?

The mass of the objects does not directly affect the time it takes for them to reach a specific distance. However, it can indirectly impact the time by affecting the acceleration of the objects. According to Newton's second law of motion, F = ma, an object's acceleration is directly proportional to the net force acting on it and inversely proportional to its mass. Therefore, a heavier object may have a slower acceleration compared to a lighter object, which can affect the time it takes to reach a specific distance.

5. Can kinematics equations be used for objects that are not moving at a constant velocity?

Yes, kinematics equations can be used for objects that are not moving at a constant velocity. In these cases, the equations will need to be modified to account for the object's changing velocity. This can be done by using the average velocity over a given time interval or by using calculus to find the instantaneous velocity at a specific time. It is important to carefully consider the motion of the object and select the appropriate equation to accurately calculate the time taken to reach a specific distance.

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