Kinematics: Motion in One Direction: Car Chase

• DracoMalfoy
In summary, the car is traveling at a constant speed of 24.0m/s, the trooper starts the chase after 1 sec has elapsed, and the final velocity of the car is not determined until after the two vehicles have reached their respective positions.
DracoMalfoy

Homework Statement

A car traveling at a constant speed of 24.0m/s passes a trooper hidden behind a billboard. One second after the speeding car passes the billboard, the trooper sets off in a chase with a constant acceleration of 3.0m/s^2.

A) How long does it take the trooper to overtake the speeding car?

B) How fast is the trooper going at the time?

Homework Equations

• Vf = Vi+a(t)
• Δd = Vi(t)+1/2(a)(t)^2
• Vf^2 = Vi^2+2(a)(Δd)
• Average Velocity: Δd/Δt
• Average Acceleration: Vf-Vi/Tf-Ti
Vf: Final Velocity
a: Acceleration
t: Time
Vi: Initial Velocity
Δd: Displacement

The Attempt at a Solution

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I tried to draw this out first. I know that the Initial Velocity for the trooper has to be 0m/s since they stay hidden behind a billboard before the car passes. and the Acceleration is 3.00m/s^2. I think that a is asking for the time... and I'm guessing that the second question is asking for Final Velocity...

Trooper

Vi: 0m/s
a: 3.00m/s^2
t: ?
Vf: ?

But is 24.0m/s the final velocity for the Car? Or the Initial? Or both? And do I look for the final velocity of the trooper first?

Delta2
The car is at constant speed for the whole time. When are their positions equal?

Cutter Ketch said:
The car is at constant speed for the whole time. When are their positions equal?

Im not sure where to start to solve this. Do they each require a separate equation?

Cutter Ketch said:
When are their positions equal?
Hint, hint

DracoMalfoy said:
Im not sure where to start to solve this. Do they each require a separate equation?
Yes exactly, write down one equation of distance as function of time for the speeding car, and another equation for the trooper. Take as t=0 the moment the speeding car passes the billboard. Make notice that the trooper starts the chase after 1sec has elapsed in order to make the correct equation of distance for the trooper.
Once you make the two equations equate the right hand sides of the two equations to get a third equation which will have one unknown the time t at which the trooper reaches the speeding car. You got to solve that 3rd equation.

DracoMalfoy said:
Im not sure where to start to solve this. Do they each require a separate equation?

Draw velocity time graphs for the two vehicles - that is the best place to start.

DracoMalfoy said:
Im not sure where to start to solve this. Do they each require a separate equation?

Instead of two separate equations you could use one single equation for the distance between the two cars.

Ray Vickson said:
Instead of two separate equations you could use one single equation for the distance between the two cars.
This single equation can be made by subtracting the two separate equations of distance. But it can be made in a more straightforward manner by using the concept of relative velocity, is that what you had in mind?

Delta² said:
This single equation can be made by subtracting the two separate equations of distance. But it can be made in a more straightforward manner by using the concept of relative velocity, is that what you had in mind?

I am leaving all the details for the OP to supply. Hints are the most I am willing to give.

Ray Vickson said:
I am leaving all the details for the OP to supply. Hints are the most I am willing to give.

You are all talking to yourselves. Delta told him exactly what to do in post 5, and the OP hasn’t been heard from since.

1. What is kinematics?

Kinematics is a branch of physics that studies the motion of objects without considering the forces that cause the motion.

2. What is motion in one direction?

Motion in one direction refers to the movement of an object along a straight line without changing direction.

3. How is kinematics used in a car chase?

Kinematics can be used to analyze and predict the motion of both the pursued and pursuing vehicles in a car chase, such as their speed, acceleration, and distance traveled.

4. What factors affect the motion of a car in a chase?

The motion of a car in a chase can be affected by various factors, including the engine power, friction, air resistance, and the driver's skill.

5. How is the concept of velocity used in a car chase?

Velocity, which is the rate of change of an object's position, is an important concept in a car chase as it can help determine the speed and direction of the vehicles involved.

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