Two particles are moving along x-axis. Particle-1 starts from `x=-10 m` with velocity `4 m//s` along negative x-direction and acceleration `2 m//s^2` along positive x-direction. Particle-2 starts from `x=+2 m` with velocity `6 m//s` along positive x-direction and acceleration `2 m//s^2` along negative x-direction.
(a) Find the time when they collide.
(b) Find the x-coordinates where they collide. Both start simultaneously.

Answer

A, B

Explanation

(a)
Particle-1 is behind the particle-2 at a distance of `12 m`. So, particle-1 will collide particle-2, if
`S_1=S_2+12 rArr :. u_1t+1/2a_1t^2=u_2t+1/2a_2t^2+12`
But now we will substitute the values of `u_1,u_2, a_1` and `a_2` with sign
`:. (-4)t+1/2(+2)t^2=(+6)t+1/2(-2)t^2+12`
Solving this equation, we get positive value of time,
`t=6s`
(b) At the time of collision, `S_1=u_1t+1/2a_1t^2=(-4)(6)+1/2(+2)(6)^2=+12 m`
At the time of collision, x-coordinate of particle`-1:`
`x_1=("Initial x-coordinate of particle-1")+S_1`
` = -10+12=+2m`
Since, they collide at the same point. Hence,
`x_2 = x_1 = +2m`