Question

Ima Hurryin is approaching a stoplight moving with a velocity of +30.0 m/s. The light turns yellow, and Ima applies the brakes and skids to a stop (vf = 0). If Ima's acceleration is -8.00 m/s2, then determine the displacement of the car during the skidding process.

a. 56.3 m
b. 120 m
c. 240 m

Answer 1

The car, initially moving with a velocity of +30.0 m/s, skids to a stop due to an acceleration of -8.00 m/s^2, resulting in a displacement of approximately 56.3 m.

Step-by-step explanation:

You're asking about the displacement of a car, Ima Hurryin's vehicle, which skids to a stop after applying brakes. We're given that the initial velocity (vi) is +30.0 m/s, the final velocity (vf) is 0 m/s (since the car stops), and the acceleration (a) is -8.00 m/s2 (deceleration, hence negative). We can use the kinematic equation:

vf2 = vi2 + 2aΔx

By rearranging this to solve for displacement (Δx), and substituting in the given values:

0 = (30.0 m/s)2 + 2(-8.00 m/s2)Δx

This simplifies to:

Δx = -(30.0 m/s)2 / (2*-8.00 m/s2)

Δx = 900 m2/s2 / 16.00 m/s2

Δx = 56.25 m

Therefore, the displacement of the car during the skidding process is approximately 56.3 m, which means the correct answer is (a) 56.3 m.