Question

18 multiple choice 1 point a car starts at rest and starts to accelerate at a meters per second per second. the car experiences a displacement of δx. determine an expression for the final velocity of the car when it has traveled this distance in terms of the variables given in the problem. a(δx) \\(\frac{a}{2δx}\\) \\(\frac{a}{δx}\\) \\(sqrt{2a(δx)}\\) \\(a^2(δx)^2\\)

Explanation:

Step1: Recall kinematic equation

We use the kinematic equation for motion with constant acceleration: \( v_f^2 = v_i^2 + 2a\Delta x \), where \( v_i \) is initial velocity, \( v_f \) is final velocity, \( a \) is acceleration, and \( \Delta x \) is displacement.

Step2: Substitute initial velocity

The car starts at rest, so \( v_i = 0 \). Substituting into the equation: \( v_f^2 = 0 + 2a\Delta x \).

Step3: Solve for final velocity

Take the square root of both sides: \( v_f = \sqrt{2a\Delta x} \).

Answer:

\(\boldsymbol{\sqrt{2a(\Delta x)}}\) (corresponding to the option with this expression)