2 bodies ar kept at a distance of 500 mtrs from each othe(at rest).they start accelerating towards each other?

Question

at10m/s and 4m/s.How will we find out when they will collide?(plzz give process and answer)

at 10m/s^2 and 12m/s^2.How will we know wen they'll collide(time)?

Answer 1

Assuming you mean: "accelerating at 10 m/s^2 and 4 m/s^2"

Let body 1 be at the origin, and let body 2 be 500 meters away on the x axis.

For body 1:

d = do + Vot + (1/2)a1t^2
where do = 0 (the initial displacement)
Vo = 0 (the initial velocity)
take a1 = 10m/s^2

d(body1) = 5t^2


For body 2:

d = do + Vot + (1/2)a2t^2
where do = 500 (the initial displacement)
Vo = 0 (the initial velocity)
take a2 = -4m/s^2

d(body2) = 500 -2t^2

now, they will collide when d(body1) = d(body2)

5t^2 = 500 - 2t^2

7t^2 = 500

t = 10sqrt(5/7)
t = 8.452 seconds

*Remarks: For the answer you seek it makes no difference which acceleration is assigned to which body. That is you get the same time if a1 = 4 m/s^2 and a2 = 10 m/s^2.

However, if you wanted to know precisely WHERE they collide, then which acceleration goes to which body matters.

Answer 2

Sorry but that is not acceleration but a velocity. m/s is unit of velocity. So, if we assume that they start moving instantaneously with those velocities towards each other, their relative velocity will be 14 m/s and we have the distance between them as

s = 500 - 14.t where t is the time in seconds.

At the moment of collision, s=0 and so we have

14.t = 500 or t = 35.714 seconds (upto 3 decimals).

This is a question in relative velocity.