Final answer:
Bodies A and B will meet after 45 seconds, traveling a distance of 360 meters. They will have final velocities of 9 m/s and 4.5 m/s, respectively.
Step-by-step explanation:
a) When will the bodies meet again?
To find the time at which the bodies will meet, we need to set up equations for the motion of each body.
For body A:
Using the equation for acceleration: vf = vi + at
Since body A starts from rest (vi = 0), the equation simplifies to: vf = at
For body B:
Using the equations for constant velocity and uniform deceleration:
vf = vi + at
Since body B starts with an initial velocity (vi = 9), the equation becomes: vf = 9 - at
To find when the bodies will meet, we need to set the final velocities of both bodies equal to each other:
at = 9 - at
2at = 9
t = 9 / (2a)
Substituting the given values for acceleration:
t = 9 / (2 * 0.2) = 45 seconds
b) How far will they go until they meet?
To find the distance traveled by both bodies until they meet, we can use the equation for distance:
d = vi*t + 0.5*a*t^2
For body A:
dA = 0*t + 0.5*0.2*t^2 = 0.1t^2
For body B:
dB = 9t - 0.5*0.1*t^2 = 9t - 0.05t^2
To find the distance when they meet, we set dA equal to dB:
0.1t^2 = 9t - 0.05t^2
0.15t^2 = 9t
0.15t = 9
t = 60 seconds
Substituting the value of t back into the equation for distance:
d = 0.1(60)^2 = 360 meters
c) How many speeds will they have at the meeting place?
Both bodies will have only one speed at the meeting place, which is the final velocity when they meet. Body A's final velocity can be found using the equation vf = at:
vfA = 0.2 * 45 = 9 m/s
Body B's final velocity can be found using the equation vf = 9 - at:
vfB = 9 - (0.1 * 45) = 9 - 4.5 = 4.5 m/s