A 1720-kg car is traveling with a speed of 15.0 m/s. What is the magnitude of the horizontal net force that is required to bring the car to a halt in a distance of 47.0 m?
v = 15-at
v=0 when t = 15/a
47 = 1/2 at^2
so, a = -225/94
F = ma
To find the magnitude of the horizontal net force required to bring the car to a halt, we can use the equation:
Force = (mass × acceleration)
Since the car needs to come to a halt, its final velocity will be 0 m/s. Therefore, the change in velocity (Δv) is equal to the initial velocity (15.0 m/s) minus the final velocity (0 m/s), which is 15.0 m/s.
To find the acceleration, we can use the equation:
Acceleration = (change in velocity / time)
However, we don't have the time information in this problem. Instead, we can use another equation relating distance and acceleration:
Distance = (initial velocity × time) + (1/2 × acceleration × time^2)
Since we know the distance (47.0 m) and the initial velocity (15.0 m/s), we can rearrange the equation to solve for time:
47.0 m = (15.0 m/s × time) + (1/2 × acceleration × time^2)
This is a quadratic equation, and we need to solve for time. By using the quadratic formula, we can find the time it takes for the car to come to a stop.
Once we have the time, we can substitute it into the equation for acceleration:
Acceleration = (change in velocity / time)
Now that we have the acceleration, we can calculate the magnitude of the horizontal net force:
Force = (mass × acceleration)
By following these steps, we can find the magnitude of the horizontal net force required to bring the car to a halt in a distance of 47.0 m.