Question

A 1500 kg car skids to a halt on a wet road where ${\mu }_k$$=0.50$. How fast was the car traveling if it leaves role="math" localid="1648126746388" $65m$-long skid marks?

Short answer

The speed of the car at the moment it skidded is$25.69m/s$

Step-by-step solution

Content Introduction

Velocity is a mechanical number that indicates the change in distance of an object in unit time in a specified direction. The metric unit is the meter per second. It explains how the thing moves.

Content Explanation

Using Newton's second law

Here, $F_g$is the gravitational force, $m$is the mass, $a$is the acceleration.

Substitute the values, where

$$\begin{gathered} m=1500kg \\ a=10m/s \end{gathered}$$

$$\begin{gathered} F_g=ma \\ {F}_g=\left(1500\right)\left(10\right) \\ {F}_g=15000N \end{gathered}$$

Now$$\begin{gathered} F_f=\mu F_n \\ {F}_f=(0.5)\left(1500\right) \\ {F}_f=7500N \end{gathered}$$

To find acceleration we use

$A=5m/s^2$

The initial velocity , here$V_f=0,d=65m,a=10$

$$\begin{gathered} V_f=V_i+2ad \\ 2ad=V_i \\ =25.69m/s \end{gathered}$$