Answer:
It takes the wolf 3 s to move as fast as the rabbit.
The wolf is 9 m from the rabbit when it reaches a speed of 6 m/s
Step-by-step explanation:
The equations for the position and velocity of objects moving in a straight line are as follows:
x = x0 + v0 · t + 1/2 · a · t²
v = v0 + a · t
Where:
x = position of the object at time t
x0 = initial position of the object
t = time
v0 = initial speed
a = acceleration
v = velocity of the object at time t
For the first question, let´s use the equation of velocity of the wolf to find at which time its velocity is the same as the velocity of the rabbit ( 6 m/s):
v = v0 + a · t (v0 = 0 because the wolf starts at rest)
6 m/s = 0 + 2.0 m/s² · t
t = 3 s
Now, with this calculated time, let´s obtain the position of the wolf:
x = x0 + v0 · t + 1/2 · a · t² (Placing the center of the frame of reference at the point when the wolf starts running makes x0 = 0)
x = 1/2 · a · t²
x = 1/2 · 2.0 m/s² · (3 s)²
x = 9 m
Now, let´s calculate the position of the rabbit. Notice that a = 0. Then:
x = x0 + v · t x0 = 0
x = v · t
x = 6 m/s · 3 s = 18 m
The wolf is (18 m - 9 m) 9 m from the rabbit when it reaches a speed of 6 m/s