Question

A car skids a distance of $54m$ on a dry road. What was the velocity of the car when the skid began if the coefficient of friction between the tires and the road is $.46$?

• A. $16m/s$
• B. $22m/s$
• C. $28m/s$
• D. $34m/s$
• E. Velocity cannot be determined with the information given

Answer 1

The correct option is B $22m/s$

Given : $\mu =0.46$

Let the mass and initial velocity of the car be $m$ and $u$ respectively.

Final velocity of the car is zero i.e $v=0m/s$

Skidding distance $S=54$ m

Thus frictional force $f=\mu mg$

$\therefore$ Acceleration of the car $a=-\frac{\mu mg}{m}=-\mu g=0.46\times 9.8=-4.5m/s^2$

Using $v^2-u^2=2aS$

OR $0-u^2=2(-4.5)\times 54$ $⟹u=\sqrt{2\times 4.5\times 54}=22$ $m/s$