Question

Two cars A and B are travelling in the same direction with velocities v_A and v_B(v_A > v_B). When the car is at a distance s behind car B, then the drivers of car A apply the brakes producing uniform retardation a, and there will be no collision when ______.

विकल्प

• `"s" ≤ ("v"_"A" - "v"_"B")/2`

• `"s" ≤ ("v"_"A" - "v"_"B")^2/(2"a")`

• `"s" ≤ ("v"_"A" - "v"_"B")^2`

• `"s" = ("v"_"A" - "v"_"B")^2/"a"`

Answer 1

Two cars A and B are travelling in the same direction with velocities v_A and v_B(v_A > v_B). When the car is at a distance s behind car B, then the drivers of car A apply the brakes producing uniform retardation a, and there will be no collision when `underlinebb("s" ≤ ("v"_"A" - "v"_"B")^2/(2"a"))`.

Explanation:

For no collision, the speed of car A should be reduced to v_B before the cars meet, i.e. final relative velocity of car A with respect to car B is zero, i.e.

`"v"_"relative" = 0`

Here, initial relative velocity, `"u"_"r" = "v"_"A" - "v"_"B"`

Relative acceleration, `"a"_"r"` = -a - 0 = -a

Let relative displacement be s_r.

Thus, from third equation of motion, we get

`"v"_"relative"^2 = "u"_"r"^2 + 2"a"_"r""s"_"r"`

= `("v"_"A" - "v"_"B")^2 - 2"as"_"r"`

⇒ `"s"_"r" = ("v"_"A" - "v"_"B")^2/(2"a")`

For no collision, s ≤ s_r

i.e., `"s" ≤ ("v"_"A" - "v"_"B")^2/(2"a")`