Question

There are 2 objects, object A has acceleration a= -2 m/s, initial position Xo = 0, and initial velocity Vo = 20. Object B has velocity V = 10 m/s, and after 10 seconds, its position is X(10s) = -1365

Calculate:

A) Velocity when they encounter (when they meet)
B) Position of encouter
C) Time of encounter

Answer 1

Part A:  Given that the initial velocity of object A is V_o = 20 m/s, position is X_o = 0 and acceleration is a = -2 m/s. The position of object A after 10 s is,

  

And the velocity of object after 10 s is,

  

  

  

Hence the object A will stop after 10 s.

Now the object B's position is X_{(10 s)}(B) = -1365 m and uniform velocity is V = 10 m/s after 10 s. Thus when they meet the velocity of object A will be 0 m/s and the velocity of object B will be 10 m/s.

Part B: As the object A's velocity becomes zero after covering distance X = 100 m. Thus the object B will meet object A at X = 100 m. Hence the poistion of encounter is X = 100 m.

Part C: The distance needed to cover by object B to meet object A is,

Thus the time taken by object B is,

  

Therefore the time of encounter is,