# Problem: A car traveling 56.0 km/h is 24.0 m from a barrier when the driver slams on the brakes. The car hits the barrier 2.00 s later.(a) What is the magnitude of the car’s constant acceleration before impact?(b) How fast is the car traveling at impact?

###### FREE Expert Solution
96% (408 ratings)
###### FREE Expert Solution

In this problem, we are required to calculate the constant acceleration and velocity before impact.

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:

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

96% (408 ratings) ###### Problem Details

A car traveling 56.0 km/h is 24.0 m from a barrier when the driver slams on the brakes. The car hits the barrier 2.00 s later.
(a) What is the magnitude of the car’s constant acceleration before impact?
(b) How fast is the car traveling at impact?