Question

H. Two objects start moving at the same time. Object A is initially at x x = 8 m and starts moving to the left at constant speed of 2 m/s and object B is initially at x2 m and starts moving to the right at a 1-1-1- constant speed of 3 m/s. Use the coordinate axes on the right to plot the position vs. time for both objects (for at least 4 seconds) then use your plot to identify the position and time when the two objects pass each a. other. Write your answers below. b. Use kinematics equations to calculate the position and time when the two objects pass each other to double check your work in a above.

Answer 1

(A) From the plot, the crossing point is at time t = 2 sec and position x = 4 m.

(B) From the Kinematic equations,

let $X_{OA} and X_{OB}$ be the initial position of the objects,

from the kinematic equation ,  

  $X_{A} = X_{OA} + v_{A}t$

$X_{B} = X_{OB} + v_{B}t$

from both the equations crossing point when the positions are equal thus;

$X_{OA} + v_{A}t = X_{OB} + v_{B}t$

$t = X_{OA} - X_{OB} / (v_{B} - v_{A})$ = (8 - (-2)) / (3 - (-2)) = 2 sec

at t = 2 sec

Position $X_{A} = X_{OA} + v_{A}t$ = 8 + (-2)*2 = 4 m

thus position and time of the crossing point are same from both the methods.