# Minimization physics problem

1. Sep 9, 2009

### ttja

1. The problem statement, all variables and given/known data
a A sportscar can accelerate uniformly to 120 mi/h in 30s. Its maximum braking rate cannot exceed 0.7g. what is the minimum time required to go 1/2 mi, assuming it begins and ends at rest?

2. Relevant equations
I drew a graph of v(t) vs t. where the initial acc. goes up to a certain time, t1, then decelerate to a rest at t2.

3. The attempt at a solution

acc= 4 mi/min
V1 = 4t

For convenience i drew another graph for when the car dec. Therefore:

acc= -0.7g
V2 = 4t1 - 0.7gt

Integrate:

d = 0.5 = int ( 4t, t, 0, t1) + int (4t1 - 0.7gt, t, 0, t2)

=> 2t1^2 + 4t1t2 - 0.7g/2 t2^2

Here is where i got lost. i know that t = t1 + t2 but i dont know how to derive t with its components to get the minimum time. please help and thank you.

2. Sep 9, 2009

### hotvette

Re: Minimization

Interesting problem. You can determine t2 in terms of t1 because the velocity must be zero in the end. Other considerations are less than max deceleration and coast time between acceleration and deceleration.

Last edited: Sep 9, 2009