Collision

The two bodies, whose initial distance is 240 m, move evenly against each other consistently. The first body has an initial velocity of 4 m/s and an acceleration of 3 m/s2, the second body has an initial speed of 6 m/s and an acceleration of 2 m/s2. Find the time of collision between the bodies and the collision distance from the initial position of the first body.

Correct result:

t =  8 s
s1 =  128 m

Solution:

v1=4 m/s a1=3 m/s2  v2=6 m/s a2=2 m/s2  s=240 m  s=s1+s2 s=(v1+v2)t+12a1 t2+12a2 t2  240=(4+6)t+0.5(3+2)t2  240=(4+6) t+0.5 (3+2) t2 2.5t210t+240=0 2.5t2+10t240=0  a=2.5;b=10;c=240 D=b24ac=10242.5(240)=2500 D>0  t1,2=b±D2a=10±25005 t1,2=10±505 t1,2=2±10 t1=8 t2=12   Factored form of the equation:  2.5(t8)(t+12)=0  t=t1=8=8 s

Our quadratic equation calculator calculates it.

s1=v1 t+12 a1 t2=4 8+12 3 82=128=128 m s2=v2 t+12 a2 t2=6 8+12 2 82=112 m s3=s1+s2=128+112=240 m



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