Velocity, acceleration, displacement

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Homework Help Overview

The problem involves a cab driver who accelerates to a speed limit and then decelerates while traveling a total distance of 2.00 km. The relationship between the magnitudes of acceleration and deceleration is specified, with the deceleration being three times that of the acceleration. The objective is to determine the lengths of the acceleration and deceleration phases.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants express uncertainty about how to start the problem, with one noting difficulties in setting up equations due to having more variables than equations. Another suggests using the equation V² = 2*a*x and proposes that the acceleration phase is represented by x and the deceleration phase by (2 - x). Questions arise regarding the equality of velocities at the transition between acceleration and deceleration phases.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem and questioning the assumptions about the velocities during the acceleration and deceleration phases. Some guidance has been offered regarding the use of specific equations, but no consensus has been reached on the approach to take.

Contextual Notes

Participants are grappling with the implications of the relationships between acceleration and deceleration, as well as the initial and final velocities in the context of the problem. There is a noted lack of clarity regarding the setup of the equations and the definitions of variables involved.

rphung
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Homework Statement


a cab driver picks up a customer and delivers her 2.00km away, on a straight route. The driver accelerates to the speed limit and, on reaching it, begins to decelerate at once. the magnitude of the deceleration is three times the magnitude of the acceleration. find the lengths of the acceleration and deceleration phases.




Homework Equations


vf=vi+at
x=xi+vit+.5at^2


The Attempt at a Solution


I honestly don't know where to begin. I tried setting up multiple equations but i keep getting more variables then equations.
 
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rphung said:

Homework Statement


a cab driver picks up a customer and delivers her 2.00km away, on a straight route. The driver accelerates to the speed limit and, on reaching it, begins to decelerate at once. the magnitude of the deceleration is three times the magnitude of the acceleration. find the lengths of the acceleration and deceleration phases.

Homework Equations


vf=vi+at
x=xi+vit+.5at^2

The Attempt at a Solution


I honestly don't know where to begin. I tried setting up multiple equations but i keep getting more variables then equations.

Consider using the equation V2 = 2*a*x
The acceleration phase is x and the deceleration distance is (2 - x) right?
Since the V is the same:

2*a*x = 2*3a*(2-x)
 
can you explain why the v's are the same?

I thought the equation was vf^2=vi^2+2ad and when the car starts deaccelerating the vi is some unknown velocity while the vf will be 0
 
rphung said:
can you explain why the v's are the same?

I thought the equation was vf^2=vi^2+2ad and when the car starts deaccelerating the vi is some unknown velocity while the vf will be 0

Sure.

You have an acceleration phase. It gets to the speed limit from 0. That would be the first equation.
The second is from the speed limit back to 0. Same speed limit. Same speed. Then you can set the two equal.
 

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