Question

Police investigators, examining the scene of an accident involving two cars, measure 72-mlong skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.

Answer 1

Answer:

The initial speed of car is 33.6 $\frac{m}{s}$

Explanation:

Given :

Distance travel by cars $x = 72$ m

Coefficient of kinetic friction $\mu _{k} = 0.80$

From the equation of kinematics,

   $v^{2} - v_{o} ^{2} = 2ax$

Where $v_{o} =$ final speed here it is zero ( $v_{o} = 0$ ), $a =$ acceleration of car

From FBD diagram we can write,

$ma =- \mu _{k} mg$

Here minus sign represent friction oppose the motion,

   $a = -\mu_{k} g$

   $a = -7.84 \frac{m}{s^{2} }$               ( ∵ $g = 9.8 \frac{m}{s^{2} }$ )

Put the value of acceleration in above equation and find initial velocity,

  $v_{o}^{2} = -2 \times (-7.84) \times 72$

  $v_{o}^{2} = 1128.96$

  $v_{o}^{} = 33.6$ $\frac{m}{s}$

Therefore, the initial speed of car is 33.6 $\frac{m}{s}$