79.3k views
4 votes
Perrysburg Science

Name: Leigha Baldwin
4) You are driving a car, traveling at a constant velocity of 25 m/s, when you see a child chase a ball
into the street. It takes 0.45 s for you to react and apply the brakes. As a result, the car slows with a
steady acceleration of 8.5 m/s2 and comes to a stop. What is the total distance the car moves before it
stops?
Sketch the problem and label known and unknown variables: NOTE: 2 parts to this problem
Initial:
Xe =
Vo =
to =
Middle:
X1 =
V1 =
t1 =
Final:
X2 =
V2 =
T2=

A) 5.625 meters
B) 11.25 meters
C) 25.45 meters
D) 32.625 meters

User Ilhicas
by
8.3k points

1 Answer

6 votes

Final answer:

The total distance the car moves before it stops is calculated by combining the distance covered during the driver's reaction time and the distance covered while decelerating to a stop, which is not amongst the given options.

Step-by-step explanation:

To find the total distance the car moves before it stops, we need to consider two phases: the distance covered during the reaction time and the distance covered while decelerating to a stop. The car initially travels at a constant velocity of 25 m/s and takes 0.45 s to react. During this reaction time, the car continues moving at the constant velocity. So, the distance covered during reaction time (Xr) is calculated using:


Xr = Vo × tr


Xr = 25 m/s × 0.45 s = 11.25 meters

Next, we calculate the distance covered during deceleration (Xd) until the car stops. As the car stops, the final velocity (Vf) is 0 m/s, and the acceleration (a) is -8.5 m/s2. The initial velocity (Vo) during deceleration is the same as the constant velocity before the reaction time. To calculate this distance, we use the kinematic equation:


Vf2 = Vo2 + 2 × a × Xd


0 = (25 m/s)2 + 2 × (-8.5 m/s2) × Xd


Xd = (25 m/s)2 / (2 × 8.5 m/s2)


Xd = 625 / 17 = 36.7647 meters

Finally, to find the total distance (Xt), we add the distances for the reaction time and deceleration phases together:


Xt = Xr + Xd


Xt = 11.25 m + 36.7647 m


Xt = 48.0147 meters

Therefore, the correct answer is not listed among the options provided by the student and needs to be recalculated based on the factually accurate values used in this explanation.

User Kumar Mangalam
by
7.6k points