Question

It was once recorded that a Jaguar left skid marks that were 20m in length. Assuming that the jaguar skidded to stop with a constant acceleration of $-3.90{ m }/{ { s }^{ 2 } }$, determine the speed of the Jaguar before it began to skid.
A). $47.6{ m }/{ s }$
B). $38.2{ m }/{ s }$
C). $54.6{ m }/{ s }$
D). $57.6{ m }/{ s }$

Answer 1

This problem can be solved by one of the kinematic equations. As time is not mentioned in the question, only one of the equations can be used to solve this problem which is not dependent on time. Substitute the given values in the equation and obtain the initial speed of Jaguar before it began to skid.

Complete step-by-step solution:
Given: Displacement d= 20m
Acceleration a=$-3.90{ m }/{ { s }^{ 2 } }$
Final velocity ${ v }_{ f }$= 0
Kinematics Equation is given as,
${ v }_{ f }^{ 2 }={ v }_{ i }^{ 2 }+2ad$
$\therefore{ v }_{ i }^{ 2 }={ v }_{ f }^{ 2 }-2ad$
Substituting the values in above equation we get,
${ v }_{ i }^{ 2 }=0-(2\times (-3.90)\times 290)$
${ \Rightarrow v }_{ i }^{ 2 }=2262$
${ \Rightarrow v }_{ i }=47.56$
Therefore, the speed of the Jaguar before it began to skid was $47.56{ m }/{ s }$.
Hence, the correct answer is option A i.e. $47.6{ m }/{ s }$.

Note: Kinematic equations can be used to predict unknown information about an object’s motion if other information is known. There are four equations of kinematics. Out of those four equations, three are dependent on time while the fourth is independent of time.