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 0.70 s and that your car brakes with constant acceleration.
How far are you from the intersection when you begin to apply the brakes?
What acceleration will bring you to rest right at the intersection?
How long does it take you to stop?
a. d = 110-Vo*t = 110 - 20*0.7 = 96 m.
b. a = (V^2-Vo^2)/2d = (0-20^2)/192 =
-2.08 m/s^2.
c. V = Vo + a*t = 0
t = -Vo/a = -20/-2.08 = 9.60 s.
Where from the 192.
Well, well, well! Looks like you've got yourself in a bit of a pickle. Let's crunch some numbers and clown around with some physics!
To find out how far you are from the intersection when you start braking, we need to get your reaction time out of the way. You're traveling at a speed of 20 m/s, and your reaction time is 0.70 s. In that time, you would have traveled a distance of 20 m/s * 0.70 s = 14 meters. Yikes! That's a decent distance to be getting closer to an intersection!
Now, to figure out the acceleration required to bring you to rest right at the intersection, we have to know the distance remaining and the time it takes for you to come to a stop. You're 110 meters away from the intersection. So, the distance remaining after your reaction time is 110 m - 14 m = 96 meters.
Now, here comes the physics rollercoaster! We know that the initial velocity is 20 m/s, the final velocity is 0 m/s (because that's when you're gonna stop), and the distance is 96 meters. By using the equation d = (v^2 - u^2) / (2a), where d is distance, v is final velocity, u is initial velocity, and a is acceleration, we can solve for a.
Rounding up to the nearest clown unit, the acceleration required will be around 5.36 m/s^2. Buckle up, we're gonna need to hit those brakes hard!
Lastly, how long does it take you to stop? We can use the equation v = u + at, where v is final velocity, u is initial velocity, a is acceleration, and t is time. In this case, v is 0 m/s, u is 20 m/s, and a is -5.36 m/s^2 (negative because we're slowing down). Solve for t, and you'll find that it takes approximately 3.7 seconds for you to come to a stop.
Just remember, my friend, when you're driving, stay alert and avoid those clownish situations. Safety first, laughs second!
To find the distance from the intersection when you begin to apply the brakes, we need to consider your reaction time. The reaction time is the time it takes for you to perceive the red light and react by applying the brakes. In this case, the reaction time is given as 0.70 seconds.
Distance traveled during reaction time can be calculated using the formula:
Distance = Velocity * Time
So, the distance traveled during the reaction time would be:
Distance = 20 m/s * 0.70 s = 14 meters
Therefore, you are 14 meters from the intersection when you begin to apply the brakes.
To find the acceleration required to bring you to rest right at the intersection, we can use the following kinematic equation:
vf^2 = vi^2 + 2*a*d
where:
vf = final velocity (which is 0 m/s since you want to come to rest)
vi = initial velocity (which is 20 m/s)
a = acceleration
d = distance from the intersection
Rearranging the equation to solve for acceleration (a):
a = (vf^2 - vi^2) / (2*d)
Substituting the values:
a = (0^2 - 20^2) / (2 * 110)
a = (-400) / (220)
a = -1.818 m/s^2
Therefore, an acceleration of -1.818 m/s^2 will bring you to rest right at the intersection.
To find the time it takes you to stop, we can use the equation:
vf = vi + a * t
where:
vf = final velocity (0 m/s)
vi = initial velocity (20 m/s)
a = acceleration (-1.818 m/s^2)
t = time taken to stop (what we are solving for)
Rearranging the equation to solve for time (t):
t = (vf - vi) / a
Substituting the values:
t = (0 - 20) / (-1.818)
t = (-20) / (-1.818)
t ≈ 11 seconds
Therefore, it will take you approximately 11 seconds to come to a complete stop.