Answer:
To solve this problem, we will use the equation for the net force on an object, which is:
net force = mass x acceleration
We can rearrange this equation to solve for acceleration:
acceleration = net force / mass
Once we have the acceleration, we can use the equation for the motion of an object under constant acceleration:
final velocity^2 = initial velocity^2 + 2 x acceleration x distance
We can rearrange this equation to solve for the distance required to stop the car:
distance = initial velocity^2 / (2 x acceleration)
Finally, we can use the equation for average velocity to calculate the time required to travel this distance:
time = distance / average velocity
Substituting the given values into the equations:
net force = 6000 N
mass = 1200 kg
initial velocity = 10 m/s
Using the first equation:
acceleration = net force / mass
acceleration = 6000 N / 1200 kg
acceleration = 5 m/s^2
Using the second equation:
distance = initial velocity^2 / (2 x acceleration)
distance = 10 m/s^2 / (2 x 5 m/s^2)
distance = 10 m
Using the third equation:
average velocity = (initial velocity + final velocity) / 2
final velocity = 0 (since the car is coming to a stop)
average velocity = 10 m/s / 2
average velocity = 5 m/s
Using the fourth equation:
time = distance / average velocity
time = 10 m / 5 m/s
time = 2 seconds
Therefore, the time required for a 6000-newton net force to stop a 1200-kilogram car initially traveling at 10 meters per second is 2 seconds.