Two cars A and B are travelling in the same d | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) To avoid a collision,the relative velocity of car $A$ with respect to car $B$ must become zero before or at the moment the distance between them b

Vedclass · Accepted Answer

$S \geqslant \frac{(V_A - V_B)^2}{2a}$

Vedclass · Answer

(C) To avoid a collision,the relative velocity of car $A$ with respect to car $B$ must become zero before or at the moment the distance between them becomes zero. Let $u_r$ be the initial relative velocity: $u_r = V_A - V_B$. Let $a_r$ be the relative acceleration: $a_r = -a - 0 = -a$. Using the kinematic equation $v^2 = u^2 + 2as$,where $v$ is the final relative velocity $(0)$,$u$ is the initial relative velocity $(V_A - V_B)$,and $s$ is the relative displacement $S'$ required to stop: $0^2 = (V_A - V_B)^2 + 2(-a)S'$. Solving for $S'$,we get $S' = \frac{(V_A - V_B)^2}{2a}$. For no collision to occur,the initial distance $S$ must be greater than or equal to the stopping distance $S'$. Therefore,$S \geqslant \frac{(V_A - V_B)^2}{2a}$.

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 $A$ is at a distance $S$ behind the car $B$,the driver of the car $A$ applies the brakes producing a uniform retardation $a$. There will be no collision when:

Similar Questions

On a foggy day,two drivers spot each other when $80\, m$ apart. They were travelling at $70\, km/h$ and $60\, km/h$. Both apply brakes simultaneously which retard the cars at the rate of $5\, m/s^2$. Which of the following statements is correct?

At a metro station, a girl walks up a stationary escalator in $20 \,s$. If she remains stationary on the escalator, then the escalator takes her up in $30 \,s$. The time taken by her to walk up on the moving escalator will be (in $\,s$)

$A$ ball is dropped from a building of height $45 \, m$. Simultaneously,another ball is thrown up with a speed of $40 \, ms^{-1}$. Calculate the relative speed of the balls as a function of time.

$A$ body is projected vertically upward with speed $10 \, m/s$ and another at the same time with the same speed in the downward direction from the top of a tower. The magnitude of the acceleration of the first body with respect to the second is ...... $m/s^2$ (take $g = 10 \, m/s^2$).

Vedclass Test Series

Exam Paper Generator

Online Exam Module