particles colliding, prove with equations, help!?

Question

A particle P, moving along a straight line with constant acceleration 0.3m/s^2 passes a point A on the line with a velocity of 20m/s. At the instant when P passes point A, a second particle Q is 20m behind A and moving with velocity of 30m/s. prove that unless the motion of P or Q changes they will collide

Answer 1

I solved the problem by stating that P would travel distance d in time t
d=20*t+.5*.3*t*t

and Q would travel d+20 in time t
t is the time to collision

d+20=30*t
d=30*t-20
Subtract the equations and solve for t:

0=.15*t*t-10t+20
t=2.064 seconds
(the second root is superfluous)
d=41.9m

Which proves collision

j

Answer 2

Well you could write the equation for distance from A (call it D), with time (t), of particle Q

something like Dq(t) = 30t - 20

then Dp(t)=20t+0.15t^2

and find out if there is any t where Dq is greater than Dp
30t-20-20t-0.15t^2 > 0
10t - (.15t^2 +20) >0

looks like it (e.g. t =3 )

Answer 3

set up an expression for the gap between the factors as a function of time. resolve for d = 0 and if there are any actual ideas, the information is accomplished. to that end the discriminate of the quadratic in t is advantageous and there are easily 2 roots, meaning the debris will collide two times. the 1st time at .6689 sec (Q overtaking P) and later at 199.331 sec whilst P overtakes Q.

Answer 4

the velocity of q is greater then the first partile so they will colide.