Question

A motorbike is being chased by a car. The motorbike moves with the speed of $20m/s$ and has acceleration of $5m/s^2$. Whereas, the car has speed of $30m/s$ and accelerates with $3m/s^2$. If the initial separation between motorbike and car is $80m$, find the distance by which car will miss the motorbike.

• A. $55m$
• B. $30m$
• C. $35m$
• D. $40m$

Answer 1

The correct option is A $55m$

Let $v_m$ and $v_c$ be the speed of motorbike and car respectively, $a_m$ and $a_c$ be the acceleration of motorbike and car respectively and $S_{cm}$ be the distance covered by the car w.r.t motorbike.
So, from relative frame (considering only car is moving)
Speed of car w.r.t motorbike is,$v_{cm}=v_c-v_m=30-20=10m/s$
And, acceleration of the car w.r.t motorbike is,$a_{cm}=a_c-a_m=3-5=-2m/s^2$
Since the car is retarding, it will stop in some time ( w.r.t bike )
So, from equation of motion we have
$v^2=v_{cm}^2+2a_{cm}{S}_{cm}$
$⟹0={10}^2-2\times 2\times S_{cm}$
$⟹S_{cm}=25m$
Since, the initial separation between car and motorbike is $80m$ and distance chased by the car is $25m$
Thus, the distance by which car has missed the motorbike is $80-25=55m$