# Find the minimum time required to go a given distance

1. Jan 26, 2010

### phillyrand

1. The problem statement, all variables and given/known data

A sportscar, Fiasco I, can accelerate uniformly to 76 m/s in 30 s. Its maximum braking rate cannot exceed 0.60g. What is the minimum time required to go 1250 m, assuming the car begins and ends at rest?

2. Relevant equations

a = v/t
v = d/t = $$\Delta$$r/t
vavg = (vi + vf)/2 [when a is constant]

3. The attempt at a solution

accelrate1 = (76m/s) / 30s = 2.53 m/s^2
accelrate2 = - (0.60)g = - (0.6)(9.8N/kg) = -5.88N/kg = -5.88 m/s^2
ri = <0,0,0>m
rf = <1250,0,0>m
vi = <0,0,0>m/s
vf = <0,0,0>m/s

I tried breaking it up into two parts, the first being the acceleration and the second being the deceleration, but I cannot seem to get the correct answer.