Assume you are speeding down the freeway at 75 mph. The car weighs 1500 kg and the effective force of the brakes is 14400 N. The car in front of you suddenly slows down, it takes 3 seconds for the car to do so. Your initial velocity was 33.53 and your final velocity is 0. If your reaction time is 1.6 seconds, how long would it take to slow down? In meters and seconds.
F = ma, so a = -144/15 = -9.6 m/s^2
75 mi/hr = 33.53 m/s
v = Vo + at = 33.53 - 9.6t
v=0 at t=3.49
So, it will take 1.6 + 3.49 = 5.09 seconds to stop
No deceleration occurs during the first 1.6 seconds, so the distance is
s = 33.53*5.09 - 4.9*3.49^2 = 110.99 m
To find the time it takes to slow down, we can start by calculating the distance the car will travel during the reaction time.
Given:
Initial velocity (u) = 33.53 m/s
Final velocity (v) = 0 m/s
Reaction time = 1.6 seconds
We can use the formula:
Distance (s) = Initial velocity * Time
Substituting the values, we have:
Distance (s) = 33.53 m/s * 1.6 s
s = 53.65 meters
During this reaction time, the car will travel a distance of 53.65 meters before the brakes are applied.
Now, to calculate the time it takes to slow down, we need to find the deceleration (negative acceleration) using the braking force and the mass of the car.
Given:
Weight of the car (m) = 1500 kg
Effective force of brakes (F) = 14400 N
We can use Newton's second law of motion:
Force (F) = mass (m) * acceleration (a)
Rearranging the formula to find the acceleration:
Acceleration (a) = Force (F) / mass (m)
Substituting the values, we have:
Acceleration (a) = 14400 N / 1500 kg
a = 9.6 m/s^2
The negative sign indicates deceleration since the car is slowing down.
Now, let's find the time it takes for the car to slow down from 75 mph (33.53 m/s) to 0 m/s.
Given:
Initial velocity (u) = 33.53 m/s
Final velocity (v) = 0 m/s
Acceleration (a) = -9.6 m/s^2
We can use the formula:
Final velocity (v) = Initial velocity (u) + (acceleration (a) * time (t))
Rearranging the formula to find the time:
Time (t) = (Final velocity (v) - Initial velocity (u)) / acceleration (a)
Substituting the values, we have:
t = (0 m/s - 33.53 m/s) / -9.6 m/s^2
t = 3.5 seconds (approximate)
Therefore, it would take approximately 3.5 seconds to slow down from 75 mph to 0 m/s.
To summarize:
- The car will travel 53.65 meters during the 1.6-second reaction time.
- It will take approximately 3.5 seconds to slow down from 75 mph (33.53 m/s) to 0 m/s.