Question

A woman is driving at a speed of 23.0 m/s sees Bigfoot on the road ahead and applies the brakes when she is 210 meters from Bigfoot. If Bigfoot does not move and the car stops right before it hits Bigfoot, what is the acceleration provided by the car's brakes?

Answer 1

The car's brakes provide a deceleration of 1.27 m/s² to stop before hitting Bigfoot.

Step-by-step explanation:

The question asks us to determine the acceleration provided by the car's brakes to stop before hitting Bigfoot. We can use the kinematic equation for the final velocity (v), initial velocity (v0), acceleration (a), and distance (d): v^2 = v0^2 + 2ad. Since the car stops, the final velocity v = 0 m/s. The initial velocity v0 is given as 23.0 m/s, and the distance d is 210 meters. Plugging in the known values we have: 0 = (23.0 m/s)^2 + 2a(210 m), we can solve for the acceleration a.

Rearranging the equation to solve for acceleration, we get: a = -(v0^2)/(2d). Substituting the known values, we calculate the deceleration as: a = -(23.0 m/s)^2/(2 × 210 m) = -​​​​​​​​​​​​​​​a.

To provide the numerical answer, we perform the calculation: a = -(23.0 m/s)^2 / (2 × 210 m) = -1.27 m/s². Therefore, the car's brakes provide a deceleration of 1.27 m/s².