Problem: On a dry road, a car with good tires may be able to brake with a constant deceleration of 4.92 m/s. (a) How long does such a car, initially traveling at 24.6 m/s, take to stop?(b) How far does it travel in this time? (c) Graph x  versus t and v  versus t for the deceleration.

FREE Expert Solution

In this problem, we are required to calculate the time a decelerating object takes come to rest and the distance covered before stopping, given its initial velocity, v0 and the deceleration, a. We are also required to represent the motion in displacement-time and velocity-time graphs.

This is a Kinematics problem since it involves 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 kinematic equations in order to solve the problem. These are:

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

Problem Details

On a dry road, a car with good tires may be able to brake with a constant deceleration of 4.92 m/s.

(a) How long does such a car, initially traveling at 24.6 m/s, take to stop?

(b) How far does it travel in this time?

(c) Graph versus and v  versus for the deceleration.