One-Dimensional Kinematics problem

AI Thread Summary
The discussion revolves around a kinematics problem involving two cars: one decelerating at -1.9 m/s² and another moving at a constant speed of 11 m/s. The main queries include determining how close the faster car can approach the slower car before braking, the time of collision, and the distance the slower car travels before impact. Participants suggest using equations of motion to find the point of collision, but the lack of initial distance (D) complicates the calculations. The conversation emphasizes the importance of relative velocity and acceleration to solve for the initial position and time of collision. Understanding these concepts is crucial for accurately answering the posed questions.
tchronos
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Hi, i have some questions for the following problems.

A car accelerate at -1.9 m/s2. Traveling at a constant velocity of 32 m/s, this car comes up behind a car traveling at a constant velocity of11 m/s.

a) How close to the slower car can the driver of the faster car come before applying his brakes and still avoid a collision?

b) At what time does the inevitable collision of the two cars occur?

c) How far beyond its position at t = 0 does the slower car get before it is hit?

so the |a1| = 1.9 m/s2
v1 = 32 m/s
v2 = 11 m/s.

Since it accelerates in a negative direction then it is deccelerating at a constant rate. For every second the velocity with decrease by 1.9 until it crashes with the second car with has a constant velocity. Now I don't understand what the question is asking for part a)

Can anyone help? thanks
 
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Write the equations of motion for each car and then impose the conditions that fulfiled for the crash to happen.

Daniel.
 
hi thanks for the reply.
I found that the two equations for the position.

X1 = V1t + .5 at^2
X2 = D + V2t

If i set these two equal, I should find the point of collision but there are two variables and they don't give me D or T. If they have given me D then the problem will be a lot easier.

On the first problem, I want to find the D but they did not provide me with a time.
 
Try using the velocity equation for car 1 to find t.
 
Better yet, use concept of relative velocity and relative acceleration. Set the final relative position at 0 and solve for initial position.
 
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