One Dimensional Kinematics Problem

AI Thread Summary
The problem involves a Ferrari traveling at a constant speed of 35 m/s and a police officer who starts accelerating 2 seconds later at 6.5 m/s². The key to solving the problem is to establish the equations for distance traveled by both vehicles and set them equal to each other to find when the officer catches up. The Ferrari's distance can be calculated using d = vt, while the officer's distance uses d = 1/2at², accounting for the 2-second delay. The final solution indicates that the motorcycle travels 507 meters when it catches the Ferrari, although the user struggles with the calculations and understanding the time component. Understanding how to combine the two equations and solve for displacement is crucial for arriving at the correct answer.
MozAngeles
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Homework Statement


How far has the motorcycle traveled, when it catches the ferarri?
A ferrari speeding at a constant 35m/s passes a police officer at rest. 2.0 s later, the officer accelerates in pursuit at 6.5 m/s^2. How far has the motorcycle traveled, when it catches the ferarri?
I know the d=vt for the ferarri and d=1/2at^2 for the police, but what is throwing me off is the 2.0 seconds later part. Help please!


Homework Equations


d=vt for the ferarri
d=1/2at2 for the police

The Attempt at a Solution


I set vt=1/2at2
solved for t and got t=2v/a=12.769 I thought I could just add the two seconds to it, but that is wrong..
 
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You're solving for the distance the motorcycle travelled, I think in this case time is only needed to find the car's velocity. You should have all the information needed to find displacement.

Vf^2 = Vi^2 + 2ad

solve for displacement.
 
But I'm not given a final velocity. The answer turns out to be 507m I just do not know how.. I know that I have to set two equations equal to each other though
 
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