Find the minimum time required to go a given distance

[phillyrand]

Homework Statement

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?

Homework Equations

a = v/t
v = d/t = $$\Delta$$r/t
v_avg = (v_i + v_f)/2 [when a is constant]

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
r_i = <0,0,0>m
r_f = <1250,0,0>m
v_i = <0,0,0>m/s
v_f = <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.

 

[jbsteele]

acceltime = (76m/s) / (2.53m/s^2) = 30sdeceltime = (1250m) / (76m/s) = 16.4 stotaltime = 30s + 16.4s = 46.4s

 

[kerimek]

Is there a different approach I should take?

I would approach this problem by first identifying the key information given and the variables involved. The sportscar, Fiasco I, has a maximum acceleration of 76 m/s in 30 seconds and a maximum braking rate of 0.60g. The distance to be covered is 1250 m and the car starts and ends at rest.

To find the minimum time required, we can use the equation d = 1/2at^2, where d is the distance covered, a is the acceleration, and t is the time. We can also use the equation v = at, where v is the final velocity, a is the acceleration, and t is the time.

First, we can calculate the time it takes for the car to reach its maximum velocity of 76 m/s. Using the equation v = at, we get t = 76 m/s / 2.53 m/s^2 = 30 seconds. This means that it takes 30 seconds for the car to reach its maximum velocity of 76 m/s.

Next, we can calculate the time it takes for the car to decelerate from its maximum velocity to a stop. Using the equation v = at, we get t = 76 m/s / (-5.88 m/s^2) = 12.92 seconds.

Therefore, the minimum time required for the car to cover 1250 m is 30 seconds (acceleration) + 12.92 seconds (deceleration) = 42.92 seconds.

In conclusion, the minimum time required for the car to cover 1250 m is 42.92 seconds, assuming it starts and ends at rest and maintains a maximum acceleration of 76 m/s and a maximum braking rate of 0.60g.