Uniform Acceleration: Calculating Distance and Speed of a Moving Car

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Homework Help Overview

The problem involves a scenario where one car is moving at a constant speed while another car starts from rest and accelerates uniformly. The objective is to determine the distance the accelerating car travels before it overtakes the moving car and to find its speed at that moment.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the use of integrals and kinematic equations to solve the problem. There is a focus on setting initial conditions and determining the appropriate constants for the equations involved.

Discussion Status

Some participants have suggested using kinematic equations instead of integration, while others are exploring how to set initial conditions correctly. There is an ongoing exchange about the specifics of the equations and constants needed for the calculations.

Contextual Notes

Participants are navigating the constraints of initial conditions and the definitions of variables in the context of uniform acceleration and constant velocity. There is uncertainty regarding the exact equations being used and how to apply them effectively.

mugzieee
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David is driving a steady 31.0m/s when he passes Tina, who is sitting in her car at rest. Tina begins to accelerate at a steady 2.30m/s^2 at the instant when David passes.

How far does Tina drive before passing David?
What is her speed as she passes him?

i tried doing an integral for this problem but can find the limits
 
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Just do an indefinite integral and set the constant c so that it fits your initial conditions.
 
There is no need to integrate if you already know the kinematic equations for the position of an object in uniform velocity and the position of an object in uniform acceleration. You know that Tina and Dave start from the same position at some time t. Make that position the origin (0) and let that time be t=0. All you have to do now is set the positions of Tina and Dave equal to each other to see what time Tina passes Dave. Using that time in standard kinematic equations, you can go back and answer both questions about Tina.
 
what would i set c to? 31?
 
If t=0 is where they pass, and you get an equation for v(t) with a C in it, just plug in 0 for t, set v(0) to the initial velocity, and solve for C. I don't know the exact equation you have, so I can't tell you what to set C to.
 

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