The brakes of your car can provide an acceleration of 4.6m/s². You're speeding at 37.5 m/s and suddenly see a police car, so you slam the brakes. How long will it take for your car to slow down to the speed limit of 25 m/s?

• A. 0.37 s
• B. 33 s
• C. 2.7 s

Answer: (C)

Verified step by step guidance

1. Identify the initial speed of the car, \( v_i = 37.5 \text{ m/s} \), and the final speed, \( v_f = 25 \text{ m/s} \).
2. Recognize that the car is decelerating, so the acceleration \( a = -4.6 \text{ m/s}^2 \) (negative because it's slowing down).
3. Use the kinematic equation for constant acceleration: \( v_f = v_i + a \cdot t \), where \( t \) is the time it takes to slow down.
4. Rearrange the equation to solve for time \( t \): \( t = \frac{v_f - v_i}{a} \).
5. Substitute the known values into the equation: \( t = \frac{25 \text{ m/s} - 37.5 \text{ m/s}}{-4.6 \text{ m/s}^2} \) and solve for \( t \).