How Long Does It Take a Sports Car to Travel 0.5 Miles from Rest?

[xxQueenie47xx]

Hey again, I've come across yet another problem and this one doesn't even compare to the last one (I'm an idiot, haha). Anyways here it goes:

A sports car, Fiasco I, can accelerate to 120 mph in 30 seconds. Its max braking rate cannot exceed 0.7g. What is the minimum time required to go 0.50 miles, assuming it begins and ends at rest?

(that is me!)

Thanks for all your help!

 

[Brad Barker]

first word of advice: be careful of those units!

secondly: have you looked at some equations that might apply?

there are three "master" equations of kinematics (i like to think of them that way, anyway!):

$$1) v = v_0 + at$$
$$2) x = x_0 + v_0 t + \frac{1}{2} at^2$$
$$3) v^2 = v_0^2 + 2a(x-x_0).$$


which of these equations will be the most useful?

 

[Brad Barker]

oh, re-reading the question, it's a bit harder than i thought!


there are two pieces of the trip that we want to consider:

1) when the car accelerates from rest to its maximum velocity in the whole trip
2) when the car slows down from that maximum velocity to rest (at the finish line).


you have to apply the appropriate equations with the appropriate values for the constants to find the values of the variables.

and THEN you piece your answers from part 1 to part 2, by realizing that your final conditions in part 1 are the initial conditions in part 2.


(maybe sketching v vs. t or x vs. t would help a lot!)