First slide

The 3 equation for uniform acc

Question

Two cars A and B are travelling in the same direction with velocities v₁ and v₂ (v₁> v₂). 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

Moderate

A

$d < \frac{{(v_{1} - v_{2})}^{2}}{2 a}$
B

$d < \frac{v_{1}^{2} - v_{2}^{2}}{2 a}$
C

$d > \frac{{(v_{1} - v_{2})}^{2}}{2 a}$
D

$d > \frac{v_{1}^{2} - v_{2}^{2}}{2 a}$

Solution

Initial relative velocity $= v_{1} - v_{2}$ , final relative velocity = 0
From $v^{2} = u^{2} - 2 a s \Rightarrow 0 = {(v_{1} - v_{2})}^{2} - 2 \times a \times s$
$\Rightarrow$ $s = \frac{{(v_{1} - v_{2})}^{2}}{2 a}$
If the distance between 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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