Question

A car traveling at 22.4m/s skids to stop 2.55s determines the skidding distance of the car (assume uniform acceleration).

Answer 1

Hint: In a uniformly accelerated motion, the velocity of the object will be changing linearly with time, the velocity changes by the same amount over the same period of time. The average velocity is the mean of initial and final velocities and the distance traveled can be easily found as the average velocity times the time of travel. Here first, we need to know what will be the retardation or the stopping acceleration, in other words, will calculate the deceleration of the car and once we know the acceleration of the car, we can easily find out the distance traveled before coming to rest.

Complete Answer:
A car is traveling at a speed of $22.4m/s$ and skids to a stop in 2.55s
So, we have following information:
Initial speed of the car = $u = 22.4\,m/s$
Final speed of the car $ = v = 0\,m/s$ (because car stops)
Time taken to come to stopping position $ = t = \,2.55\,sec$
We have to find deceleration of car or retardation of car “a”
By using equation of motion:
$v = u + at$
$ \Rightarrow 0 = 22.4 + a(2.55)$
$ \Rightarrow a = - 8.784m/{s^2}$
Therefore, the deceleration of the car is $ - 8.784m/{s^2}$.
To determine the distance travelled before stopping can be calculated as follows:
${v^2} = {u^2} + 2as$
$ \Rightarrow 0 = {(22.4)^2} + 2( - 8.784)s$
$ \Rightarrow s = 28.56m$
Therefore, the car will travel 28.56m before stopping.

Note: The negative sign in the calculation of acceleration indicates that retardation, we should be careful with the sign convention. Deceleration is also known as retardation or negative acceleration, it is the acceleration that acts in the opposite direction of motion and is responsible for reducing the velocity of a body.