Understanding the Concepts
* Force (F): The force applied to the car is -3000 N. The negative sign indicates that the force is acting in the opposite direction of the car's motion (braking force).
* Mass (m): The mass of the car is 3000 kg.
* Initial Velocity (v_i): The car's initial velocity is 10 m/s.
* Final Velocity (v_f): The car comes to a stop, so its final velocity is 0 m/s.
* Acceleration (a): We need to calculate the acceleration caused by the braking force.
* Stopping Distance (Δx): This is what we want to find.
Calculations
1. Calculate Acceleration:
* Use Newton's Second Law: F = ma
* Rearrange to solve for acceleration: a = F/m
* Substitute the values: a = -3000 N / 3000 kg = -1 m/s² (The negative sign indicates deceleration)
2. Use Kinematics Equation:
* We can use the following kinematics equation to find the stopping distance:
* v_f² = v_i² + 2aΔx
* Rearrange to solve for Δx:
* Δx = (v_f² - v_i²) / (2a)
* Substitute the values:
* Δx = (0² - 10²) / (2 * -1) = 50 meters
Answer:
The stopping distance for the car is 50 meters.
