What will the stopping distance be for a 1,000-kg car if -2,000 N of force are applied when the car is traveling 10 m/s?
To determine the stopping distance of a car, we need to consider the forces acting on it and apply the basic principles of physics. In this case, we have the force applied to the car and its initial velocity, so we can calculate the stopping distance using the equation:
Stopping Distance = (Initial Velocity^2) / (2 * Deceleration)
First, we need to find the deceleration of the car. To do that, we have to use Newton's second law of motion, which states that force is equal to mass times acceleration:
Force = Mass * Acceleration
Rearranging the equation, we can solve for acceleration:
Acceleration = Force / Mass
In this case, the force applied is -2,000 N (negative because it opposes the car's motion), and the mass of the car is 1,000 kg. Plugging these values into the equation, we get:
Acceleration = -2,000 N / 1,000 kg = -2 m/s^2
Now we have the deceleration, and we can plug it, along with the initial velocity, into the equation for stopping distance:
Stopping Distance = (Initial Velocity^2) / (2 * Deceleration)
In this case, the initial velocity is 10 m/s. Plugging this into the equation, we get:
Stopping Distance = (10 m/s)^2 / (2 * -2 m/s^2)
Calculating this, we get:
Stopping Distance = 100 m^2/s^2 / -4 m/s^2
Stopping Distance = -25 m^2/s^2
The stopping distance is -25 m^2/s^2. Note that the negative sign indicates that the car is moving in the opposite direction of the applied force, so the value is negative.
The deceleration rate will be
a = F/m = 2 m/s^2. The time to stop is given by
t = Vo/a = (10 m/s)/(2m/s^2) = 5 s