Question

It was once recorded that a Jaguar left skid marks that were $290m$ in length. Assuming that the Jaguar skidded to a step with a constant acceleration of $- 3.90m/{s^2}$ , determine the speed of the Jaguar before it begins to skid.
(A) $47.6m/s$
(B) $38.2m/s$
(C) $54.6m/s$
(D) $57.6m/s$

Answer 1

Hint : To solve this question we need to use the third kinematic equation of motion. Then putting the values given in the question, we can get the final answer.

Formula used: The formula which has been used in solving this question is given by
${v^2} - {u^2} = 2as$ , here $v$ is the final velocity, $u$ is the initial velocity, $a$ is the uniform acceleration, and $s$ is the displacement of an object.

Complete step by step answer
The skid marks are basically marks of the tire on the road due to sudden breaking of the vehicle on the road. These occur because of sudden braking or collision of the vehicle due to which the tire of the vehicle undergoes pure sliding motion without any rotation. As the car is sliding on the road, its motion is translational. Also since the car is skidding with a uniform acceleration, all the three equations of motion are valid here.
From the third equation of motion we have
${v^2} - {u^2} = 2as$ ..................(1)
According to the question, the Jaguar left the skid marks that are of length $290m$ with a constant acceleration of $- 3.90m/{s^2}$ . Also, since the car is stopped after skidding, so the final velocity of the car is equal to zero. Therefore substituting $v = 0$ , $a = - 3.90m/{s^2}$ , and $s = 290m$ in (1) we have
${0^2} - {u^2} = 2\left( { - 3.90} \right)\left( {290} \right)$
$\Rightarrow {u^2} = 2262$
Taking square root both the sides, we finally get
$u = 47.56m/s \approx 47.6m/s$
Thus, the velocity of the Jaguar before it begins to skid is equal to $47.6m/s$ .
Hence, the correct answer is option A.

Note
Although the final velocity is not directly given to be equal to zero in this question, it is mentioned that the “Jaguar skidded to a stop”. This phrase indirectly means that the final velocity of the Jaguar is zero. We must know how to exploit the hidden information inside these types of questions.