Question

2 cars with velocities 10 m/s and 20 m/s are travelling in opposite directions, having uniform retardation of 2m/s^2 and 1m/s^2 respectively. Find minimum separation between them such that they don't collide

Answer 1

Answer:

find the sumsimplesum simplesion fivdficefivd ficefirefice fireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefireficeireficefireficefireficefireficefireficefireficefireficefirefice

Answer 2

Minimum Separation is 10 m

Explanation:

Let the Velocity of A = 10 m/s

Velocity of B = 20 m/s

Retardation of A = $-2m/s^{2}$

Retardation of B = $-1m/s^{2}$

Since, Relative Velocity of A with respect of B must be Zero,

So, $V_{R} = 0$

The Relative initial velocity of A with respect of B is $V_{A} - V_{B}$

& Relative acceleration of A with respect of B is (-2 - (-1)) = -2 + 1 = -1 m/s

Using equation $v^{2} - u^{^{2}} = 2as$

$0 = (V_{A}-V_{B})^{2}+2\times(-a)(s)$

$s = \frac{(V_{A}-V_{B})^{2}}{2a}$

$s = \frac{10 - 20}{-2a}$

$s = \frac{-10}{-1}$

s = 10 m

Minimum Separation between them is 10 m.