Question

On a foggy day, two drivers spot in front of each other when 80 metre apart. They were traveling at 70 kmph and 60 kmph. Both apply brakes simultaneously which retard the cars at the rate 5 \[{\text{m/}}{{\text{s}}^2}\]Which of the following statements is correct?
A.) The collision will be averted
B.) The collision will take place
C.) They will across each other
D.) They will just collide

Answer 1

Hint: We can solve this type of question using the Velocity equation easily. The velocity equation consists, final velocity (v) squared equals initial velocity (u) squared plus two times acceleration (a) times displacement (s).

Complete step-by-step answer:

Formula Used: \[{{\text{v}}^{\text{2}}}{\text{ - }}{{\text{u}}^{\text{2}}}{\text{ = 2as}}\]
Let’s find the distance travelled by both before they come to a halting stop.

Car 1:

\[

  {\text{u = 72kmph = 20 m/s}} \\
  {\text{a = - 5 m/}}{{\text{s}}^2} \\
  {{\text{v}}^{\text{2}}}{\text{ - }}{{\text{u}}^{\text{2}}}{\text{ = 2as}} \\
  {{\text{0}}^2} - {20^2} = 2( - 5)s \\
  s = 40{\text{ m}} \\

\]

Car 2:

\[
  {\text{u = 60 kmph = 16}}{\text{.66 m/s}} \\
  {\text{a = - 5 m/}}{{\text{s}}^2} \\
  {{\text{v}}^{\text{2}}}{\text{ - }}{{\text{u}}^{\text{2}}}{\text{ = 2as}} \\
  {{\text{0}}^2} - {16.6^2} = - 2(5)s \\
  s = 27.7{\text{ m}} \\
\]

Since they are 80m apart and the sum of both their distance is less than 80, they would stop before time. There would be no collision.

Note: The terms velocity and speed give us an understanding of how quickly or slow an object goes. Quite often, we find situations where we need to identify which of the two or more objects is moving more quickly. When they are going in the same direction on the same lane, one can quickly say the fastest of the two. Yet if their direction of motion is in the opposite direction then deciding the quickest is complicated. The magnitude of an object's velocity can be defined as the rate of change in the direction of the body in relation to a frame of reference and time. It may sound complex but velocity in a given direction is simply traveling. It is a vector quantity which means that in order to describe velocity, we need both magnitude and direction. It's SI unit is meter per second when there is a change of amplitude or direction of a body's velocity the body is considered to be accelerated.