You are driving to the grocery store at 11.9m/s. You are 169.0m from an intersection when the traffic light turns red. Assume that your reaction time is 0.730s and that your car brakes with constant acceleration. How far are you from the intersection when you begin to apply the brakes?

Question

You are driving to the grocery store at 11.9m/s. You are 169.0m from an intersection when the traffic light turns red. Assume that your reaction time is 0.730s and that your car brakes with constant acceleration. How far are you from the intersection when you begin to apply the brakes?

a). What acceleration will bring you to rest as you just reach the intersection?
b). How long does it take you to stop?

Answer 1

s= 169 - v•t₀=169-11.9•0.73=160.3 m

a=v²/2s=11.9²/2•160.3=0.44 m/s²
0=v-at
t=v/a=11.9/0.44=26.9 s.

Answer 2

I don't think b) is correct because im getting an incorrect answer

Answer 3

To find the distance from the intersection when you begin to apply the brakes, we need to consider the time it takes for you to react to the red light and the distance traveled during that time.

a) First, we'll calculate the distance traveled during your reaction time. The formula for distance is:

distance = initial velocity × time + 0.5 × acceleration × time^2

Given:
initial velocity (vi) = 11.9 m/s
time (t) = 0.730 s
acceleration (a) = ?

Plugging the values into the formula, we can solve for the distance traveled during the reaction time:

distance = 11.9 m/s × 0.730 s + 0.5 × a × (0.730 s)^2

Now we know that the total distance from the intersection when the traffic light turns red is 169.0 m. So the distance traveled during the reaction time plus the distance traveled after applying the brakes must equal 169.0 m.

Let's denote the distance traveled after applying the brakes as x:

distance + x = 169.0 m

b) To find the acceleration required to bring you to rest just as you reach the intersection, we can use the equation of motion:

velocity^2 = initial velocity^2 + 2 × acceleration × distance

Given:
initial velocity (vi) = 11.9 m/s
final velocity (vf) = 0 m/s
distance (d) = x

Plugging the values into the equation, we can solve for the acceleration:

0 = (11.9 m/s)^2 + 2 × a × x

Now we have two equations:

1) distance + x = 169.0 m
2) 0 = (11.9 m/s)^2 + 2 × a × x

We can solve this system of equations simultaneously to find both the distance when you begin to apply the brakes (x) and the acceleration required to bring you to rest just as you reach the intersection (a).