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/s^2, then determine the displacement of the car during the skidding process.

a) 56.3 m
b) 120 m
c) 240 m
d) 320 m

Answer 1

To find the displacement during the skidding of a car, one can use the kinematic equation for uniform acceleration. Applying the given initial velocity, final velocity, and deceleration values, the displacement is calculated as 56.25 meters, which corresponds to answer choice a) 56.3 m.

Step-by-step explanation:

The given problem involves determining the displacement of Ima Hurryin's car during the skidding process. This can be calculated using the kinematic equation for uniform acceleration, which is:

vf2 = vi2 + 2aΔx

Where:
vf = final velocity (0 m/s, as the car stops)
vi = initial velocity (+30.0 m/s)
a = acceleration (-8.00 m/s2, negative because it is deceleration)
Δx = displacement (the value we want to find)

By rearranging the equation to solve for Δx, we get:

Δx = (vf2 - vi2)/2a

Substituting the given values into the equation:

Δx = (0 - 30.02)/(2 * -8.00)

Δx = -900 / -16

Δx = 56.25 m

The displacement of the car during the skidding process is 56.25 m. Therefore, the answer is a) 56.3 m.