A 921kg sports car is moving rightward with a speed of 29.0m/s. The driver suddenly slams on the brakes, causing a 8347N resistive net force and the car skids to a stop. Determine the time it takes to stop the car.
Force=ma= mass*(Vf-Vi)/time
time= mass*(Vf-Vi)/force
vf=0
solve for time.
To determine the time it takes to stop the car, we can use Newton's second law of motion, which states that the net force applied on an object is equal to the product of its mass and acceleration. In this case, the net force is the resistive force applied by the brakes.
First, let's calculate the acceleration of the car. We can use the following formula:
Net force = mass x acceleration
Rearranging the formula to solve for acceleration:
Acceleration = Net force / mass
Substituting the given values:
Acceleration = 8347 N / 921 kg
Acceleration = 9.06 m/s²
Now, we can use the kinematic equation to determine the time it takes for the car to come to a stop. The equation we'll use is:
vf = vi + at
Where:
vf = final velocity (0 m/s, as the car comes to a stop)
vi = initial velocity (29.0 m/s)
a = acceleration (9.06 m/s²)
t = time
Rearranging this equation to solve for time:
t = (vf - vi) / a
Substituting the values:
t = (0 m/s - 29.0 m/s) / 9.06 m/s²
t = -29.0 m/s / 9.06 m/s²
t ≈ -3.2 s
Note: The negative sign indicates that the car is decelerating or slowing down. In this context, we're only interested in the magnitude of time, so we take the absolute value of the result.
Therefore, it takes approximately 3.2 seconds for the car to come to a stop.