Physics Problem involving Kinematics

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A typical car's brakes can achieve a maximum deceleration of less than 5 m/s², prompting a discussion on how close one can approach a stop sign before braking. The initial velocity is a crucial factor, and the problem can be expressed in terms of variables rather than specific numbers. The formula V² = Vo² + 2ax is applicable, allowing for the calculation of stopping distance in relation to initial speed and acceleration. Dimensional analysis can help estimate the braking distance, confirming that the solution can be derived mathematically. The conversation emphasizes the importance of understanding kinematic equations in solving such physics problems.
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1) A typical car's brakes can create a maximum acceleration of less than 5 m/s2 . How
close can you get to a stop sign before you start braking?

I don't think it's even doable, since there's no initial velocity. Or am I wrong?
 
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you are correct, sir. though, you could write the answer in terms of the unknown v_0.
 
Oh. So then my answer would be in variables, and not actual numbers?
 
yep. you can write the answer for the shortest braking distance in terms of the initial velocity and the acceleration... you might be able to guess it (up to a factor of 1/2) from dimensional analysis (i.e., looking at the units).
 
So can I use V^2 = Vo^2 + 2ax as the formula for solving this?
 
yeah, since you know what v has to be when the car has stopped. you can solve for x in terms of v0 and a.
 

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