Question

Two cars A and B have masses $m_A$ and $m_B$ respectively, with $m_A>m_B$. Both the cars are moving in the same direction with equal kinetic energy,. If equal braking force is applied on both, then before coming to rest

• A. A will cover a greater distance
• B. B will cover a greater distance
• C. Both will cover the same distance
• D. Distance covered by them will depend on their respective velocities

Answer 1

Answer: (C), (D)

The correct options are
C Both will cover the same distance
D Distance covered by them will depend on their respective velocities

Using second equation of motion in reverse direction $s=ut+\frac{1}{2}a{t}^2$

Distance covered by cars before coming to rest $=\frac{1}{2}a{t}^2$

where, $a=acceleration=\frac{F}{m}$

$t=time=\frac{v}{a}=\frac{vm}{F}$

So, Distance covered$=\frac{1}{2}a{t}^2=\frac{1}{2}\left(\frac{F}{m}\right)(\frac{vm}{F}{)}^2=\frac{m{v}^2}{2F}$

Since, $F_A=F_B$ and $m_A{v}_A^2=$$m_A{v}_A^2$

Distance covered by both cars are equal and it depends on their velocities.

Therefore, c and d are correct option.