Kinematics Equations Video Lessons

Concept

# Problem: A car slows down uniformly from a speed of 18.0 m/s to rest in 5.50 s. How far did it travel in that time?

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###### FREE Expert Solution

In this problem, we are required to calculate the distance covered by a decelerating object before stopping given its initial velocity, v0 and the time elapsed, t.

This is a Kinematics problem since it mentions initial velocity, v0, acceleration, a, distance covered Δx, and time, t

We'll follow the following simple steps!

1. Identify the target variable, knowns, and Unknowns for each part of the problem—remember that only 3 of the 5 variables (Δx, v0, vf, a, and t) are needed to solve any kinematics problem.
2. Choose a UAM equation with only one unknown, which should be our target variable.
3. Solve the equation for the target variable, then substitute known values and calculate the answer.

We need to remember the four UAM (kinematic) equations in order to solve the problem. These are:

$\overline{){{\mathbit{v}}}_{{\mathbit{f}}}{\mathbf{=}}{{\mathbit{v}}}_{{\mathbit{o}}}{\mathbf{+}}{\mathbit{a}}{\mathbit{t}}\phantom{\rule{0ex}{0ex}}{\mathbit{\Delta }}{\mathbit{x}}{\mathbf{=}}{\mathbf{\left(}}\frac{{\mathbit{v}}_{\mathbit{f}}\mathbf{+}{\mathbit{v}}_{\mathbit{o}}}{\mathbf{2}}{\mathbf{\right)}}{\mathbit{t}}\phantom{\rule{0ex}{0ex}}{\mathbit{\Delta }}{\mathbit{x}}{\mathbf{=}}{{\mathbit{v}}}_{{\mathbit{o}}}{\mathbit{t}}{\mathbf{+}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbit{a}}{{\mathbit{t}}}^{{\mathbf{2}}}\phantom{\rule{0ex}{0ex}}{{{\mathbit{v}}}_{{\mathbit{f}}}}^{{\mathbf{2}}}{\mathbf{=}}{{{\mathbit{v}}}_{{\mathbit{o}}}}^{{\mathbf{2}}}{\mathbf{+}}{\mathbf{2}}{\mathbit{a}}{\mathbit{\Delta }}{\mathbit{x}}}$

79% (284 ratings)
###### Problem Details

A car slows down uniformly from a speed of 18.0 m/s to rest in 5.50 s. How far did it travel in that time?