Constant acceleration and brakes

[elizabethR]

how would i do this problem...

You are driving to the grocery store at 20 m/s. You are 110 m from an intersection when the traffic light turns red. Assume that your reaction time is 0.50 s and that your car brakes with constant acceleration.

1)How far are you from the intersection when you begin to apply the brakes? I know this answer: 100m.
...i can't figure out the next two. please help me figure out the formula for this!
2)What acceleration will bring you to rest right at the intersection?
3)How long does it take you to stop?

 

[al_201314]

Since your acceleration is constant, you can use this equation:

v^2 = u^2 + 2as

Where v is your final velocity which is 0, u intial velocity, a is acceleration and s displacement.

For the 3rd part, use v = u + at where t is time taken. The value for a is the one you've found for the 2nd part.

Should give you all the answers. :)

 

[kyle8921]

1) To find the distance from the intersection when you begin to apply the brakes, we can use the formula: d = vi*t + (1/2)*a*t^2, where d is the distance, vi is the initial velocity, t is the time, and a is the acceleration. In this case, vi = 20 m/s, t = 0.50 s, and we want to solve for d. Plugging in the values, we get d = (20 m/s)*(0.50 s) + (1/2)*(a)*(0.50 s)^2 = 10 m + (1/4)*a. Since we know that the distance from the intersection is 110 m, we can set up the equation 110 m = 10 m + (1/4)*a and solve for a. This gives us a = 400 m/s^2. So, the acceleration needed to bring you to a stop at the intersection is 400 m/s^2.

2) To find the acceleration needed to bring you to a stop right at the intersection, we can use the formula v^2 = vi^2 + 2*a*d, where v is the final velocity, vi is the initial velocity, a is the acceleration, and d is the distance. In this case, v = 0 m/s, vi = 20 m/s, and d = 110 m. Plugging in the values, we get 0 m/s = (20 m/s)^2 + 2*a*(110 m). Solving for a, we get a = -200 m/s^2. This means that you need to decelerate at a rate of 200 m/s^2 to come to a stop right at the intersection.

3) To find the time it takes you to stop, we can use the formula v = vi + a*t, where v is the final velocity, vi is the initial velocity, a is the acceleration, and t is the time. In this case, v = 0 m/s, vi = 20 m/s, and a = -200 m/s^2. Solving for t, we get t = (0 m/s - 20 m/s)/(-200 m/s^2) = 0.10 s. So, it takes 0.10 s for you to stop at the intersection.