# Race Kinematics problem

1. Sep 29, 2010

### student1ds

Hi, I am unable to figure this question. Could someone help please ? A new type of race has been proposed. The object of the race is to complete the course and stop on the finish line in the minimum amount of time. The race is exactly 1 km long. The car can accelerate at 8m/s^2 and decelerate at 5m/s^2 when the brakes are applied. What is the best possible time to complete the race?

2. Sep 29, 2010

### student1ds

Re: Kinematics

I tried using the kinematics equations but the deceleration bit is throwing me off each time.

3. Sep 29, 2010

### qswdefrg

Re: Kinematics

hello person from Corsini's class.

... I don't get the question either. u__u;

4. Sep 29, 2010

### PhanthomJay

Re: Kinematics

Yes, its all in the kinematic equations and the fact that the car accelerates at 8 m/s/s over a distance d1, then decelerates over a distance d2 at 5 m/s/s, where d1 + d2 =1000 m. Hint: the car accelerates from 0 to some maximum speed, then decelerates from that same max speed to 0 at the finish line.

5. Sep 29, 2010

### student1ds

Re: Kinematics

I think I got an answer but to me it doesn't make sense. Is it possible to complete a 1 km race in 9 seconds ?

6. Sep 29, 2010

### qswdefrg

Re: Kinematics

I think I'm on the right track... but I always seem to end up with more variables than equations. :/

7. Sep 29, 2010

### PhanthomJay

Re: Kinematics

Not at an acceleration of 8m/s/s. Even if the car were to cross the finish line without applying the brakes before then, the time would be determined from d=1/2(a)(t)^2, solve t = almost 16 seconds.....so since the car is braking well before the finish line in order to stop and have no velocity at the finish line, the total time must be greater than 16 seconds.

8. Sep 29, 2010

### PhanthomJay

Re: Kinematics

One equation is d1 +d2 =1000; you'll then need a couple of the kinematic equations for each portion of the trip (d1 and d2, respectively), to solve for the time of each portion.