Kinematics: Motion in One Direction: Car Chase

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?

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?

When are their positions equal?
Hint, hint

Delta2
Homework Helper
Gold Member
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.

PeterO
Homework Helper
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.

Ray Vickson
Homework Helper
Dearly Missed
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.

Delta2
Homework Helper
Gold Member
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?

Ray Vickson