While driving a car, you see an obstruction in the road. It takes you 0.80 seconds to react and put your foot on the brake. The car is travelling at 25 m/s. If, when the brakes are applied, the acceleration is 9.3 m/s^2 [backwards], what is the total displacement of the car?
How long does it take to stop after brakes pressed:
vf=vi+at or t= 25/9.8
how far does it travel then?
d=avgvelocity/time=12.5*9.8/25=4.9 m
how far did it travel in reaction time?
d=25/.8
now add the two distances.
To find the total displacement of the car, we need to calculate the distance covered before the brakes are applied and the distance covered after the brakes are applied.
Before the brakes are applied, the car is traveling at a constant velocity. The time it takes to react and put your foot on the brake, 0.80 seconds, is the time it takes for the car to cover a certain distance.
Using the equation for distance (d) traveled at constant velocity (v) and time (t), we can calculate the distance covered before applying the brakes:
d1 = v * t1
Substituting the given values, we have:
d1 = 25 m/s * 0.80 s
d1 = 20 meters
So, the car covers 20 meters before the brakes are applied.
After the brakes are applied, the car decelerates with an acceleration of -9.3 m/s^2 (backwards). The time it takes to come to a stop is not given, but we can calculate it by using the equation for acceleration (a), final velocity (vf), initial velocity (vi), and time (t):
vf = vi + a * t
Since the final velocity is 0 m/s when the car stops, we can rearrange the equation to solve for the time:
t2 = (vf - vi) / a
Substituting the given values, we have:
t2 = (0 m/s - 25 m/s) / -9.3 m/s^2
t2 = 2.69 seconds (approximately)
So, it takes approximately 2.69 seconds for the car to come to a stop.
To calculate the distance covered after applying the brakes, we can use the equation for displacement (d) with initial velocity (vi), final velocity (vf), and acceleration (a):
d2 = (vf^2 - vi^2) / (2 * a)
Since the final velocity is 0 m/s, the equation simplifies to:
d2 = -vi^2 / (2 * a)
Substituting the given values, we have:
d2 = -25 m/s)^2 / (2 * -9.3 m/s^2)
d2 = -8.06 meters (approximately)
Since the acceleration is in the opposite direction of the initial velocity, the displacement value is negative.
Finally, to find the total displacement of the car, we add the distances covered before and after applying the brakes:
Total displacement = d1 + d2
Total displacement = 20 meters + (-8.06 meters)
Total displacement = 11.94 meters (approximately)
Therefore, the total displacement of the car is approximately 11.94 meters, with a negative sign indicating the direction (backwards) in this case.