Newton's Laws: Distance of a car accelerating, then slamming on the breaks.

In summary, in this problem, a car with a mass of 1980 kg and a net force of 32000 N accelerates down a road. At t = 12 seconds, the driver slams on the brakes to avoid hitting a deer. The coefficient of kinetic friction for the rubber on pavement is assumed to be .8. Using the equations of motion, the distance traveled by the car can be calculated by adding the distance traveled under constant acceleration, d1, and the distance traveled under constant velocity, d2. The force of friction from braking is equal to the normal force multiplied by the coefficient of kinetic friction, and the acceleration from braking is equal to the coefficient of kinetic friction multiplied by
  • #1
jillime
7
0
A car which is originally at rest accelerates down a road with a net force of 32000 N acting on a 1980 kg car. At t = 12 seconds the driver slams on the brakes to avoid hitting a deer. Calculate the distance traveled by the car.
Coefficient of kinetic friction for the rubber on pavement is assumed to be .8


F⃗ net=ΣF⃗ =ma⃗ (a = F/m)
fk=μkN

v=v0+at
x=x0+v0t+(1/2)at2
v2=v20+2aΔx
a = Δv/Δt
blablahblah

Anyone who can tell me how to start this problem?
FBD shows force of friction going -X, normal force y, weight -y.

32000 = 1980a
a = 16.16 m/s2

v = 0 + 16.16x12
v = 193.92 m/s

I obviously have to do a second xvat for t=12 seconds and onward. These net force/ Newtons laws problems are killing me because they involve a lot of creativity with choosing working equations, which I don't have.

Help please!
 
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  • #2
We know the force from braking is equal to Fn*uk.

Force braking is (1980)(9.8)*.8

acceleration from braking is therefore 9.8*.8 in the negative x direction from F=ma

d1+d2=total distance

d1:

use d1=.5at^2

d2:

use d2=v0t+.5at^2

where a is negative for the d2 equation and I found it above
 

1. How do Newton's Laws apply to the distance of a car accelerating and then slamming on the breaks?

Newton's Laws of Motion state that an object will remain at rest or continue to move at a constant velocity unless acted upon by an external force. In the case of a car accelerating and then slamming on the breaks, the external force is the friction between the tires and the road. The first law explains why the car continues to move forward before the brakes are applied, and the second law explains the change in velocity (deceleration) once the brakes are applied.

2. What is the relationship between the acceleration and distance of a car during this scenario?

The acceleration of a car is directly proportional to the distance it travels, according to Newton's second law. This means that a greater acceleration will result in a greater distance traveled before the car comes to a complete stop. It is important to note that the mass of the car also plays a role in this relationship, as a heavier car will require more force (acceleration) to come to a stop, resulting in a longer distance traveled.

3. How does the third law of motion apply to a car accelerating and then slamming on the breaks?

The third law of motion states that for every action, there is an equal and opposite reaction. In the case of a car accelerating and then braking, the action is the force applied by the engine to accelerate the car, and the reaction is the force applied by the brakes to slow down the car. These two forces are equal and opposite, causing the car to come to a stop.

4. Why does the distance traveled by a car depend on the speed at which it is traveling before braking?

The distance traveled by a car before braking is directly related to its initial speed, according to the second law of motion. This is because the force required to slow down a car is greater at higher speeds. Therefore, a car traveling at a higher speed will require more time and distance to come to a complete stop compared to a car traveling at a lower speed.

5. Can the distance traveled by a car during this scenario be calculated using Newton's Laws?

Yes, the distance traveled by a car can be calculated using Newton's Laws of Motion. By knowing the initial speed of the car, the mass of the car, and the force applied by the brakes, one can use the equations derived from Newton's Laws to calculate the distance traveled before the car comes to a stop. However, it is important to consider that other factors such as air resistance and road conditions may also affect the distance traveled by a car during this scenario.

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