Final answer:
The bodies will meet again in 30 seconds. They will travel a distance of 90 meters until they meet. At the meeting place, they will have 2 velocities: 0 m/s for body A and 6 m/s for body B.
Step-by-step explanation:
The first step is to find the time it will take for both bodies to meet.
For Body A, we can use the equation:
d = Vit + 0.5at^2
where d is the distance traveled, Vi is the initial velocity, t is the time, and a is the acceleration.
Since body A starts from rest, the equation simplifies to:
d = 0.5at^2
For Body B, we can use the equation:
d = Vi*t + 0.5at^2
where d is the distance traveled, Vi is the initial velocity, t is the time, and a is the acceleration.
Since body B starts with an initial velocity, the equation becomes:
d = Vit + 0.5at^2
We can set up the equations and solve for t:
0.5*0.2*t^2 = 9*t + 0.5*(-0.1)t^2
Simplifying and rearranging the equation, we get:
0.3t^2 - 9t = 0
By factoring out t, we get:
t(0.3t - 9) = 0
So, t = 0 or t = 30 s. Since we are looking for a time when the bodies meet, the time cannot be 0, so the bodies will meet in 30 seconds.
Next, we can find the distance they will travel until they meet.
We can use the equation:
d = Vit + 0.5at^2
Since both bodies start at the same place, the equation becomes:
d = 0.5*0.2*(30)^2 = 90 m
Finally, we can calculate the number of velocities they will have at the meeting place.
Since body A starts from rest, its final velocity will be 0. Body B starts with an initial velocity of 9 m/s and decelerates at a rate of 0.1 m/s^2. We can use the equation:
v = Vi + at
where v is the final velocity, Vi is the initial velocity, a is the acceleration, and t is the time.
Plugging in the values, we get:
v = 9 + (-0.1)*30 = 6 m/s
So, they will have 2 velocities at the meeting place: 0 m/s for body A and 6 m/s for body B.