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Standard XII

Physics

Relative Acceleration

Two cars A an...

Question

Two cars A and B are traveling in the same direction with velocities $v_{1}$ and $v_{2} (v_{1} > v_{2})$ When the car A is at a distance d ahead of the car B, the driver of the car A applied the brake producing a uniform retardation a. There will be no collision when

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Solution

The correct option is C
Step 1, Given data
Velocities are $v_{1} a n d v_{2}$
Car A is ahead of car B by distance d.
Step 2,
We can write
Initial relativity velocity $= v_{1} - v_{2}$ ,
Final relativity velocity =0
From equation of motion
$v^{2} = u^{2}$ - 2as $\Rightarrow$ 0= $(v_{1} - v_{2})^{2} - 2 \times a \times s$
After solving
$\Rightarrow s = \frac{(v_{1} - v_{2})^{2}}{2 a}$
Now we can say that
If the distance betwee two cars is 's' then collision will take place.To avoid collision
$d > s ∴$ $d > \frac{(v_{1} - v_{2})^{2}}{2 a}$
where d= actual initial distance between two cars.

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