Question

A rabbit is traveling at a steady 6 m/s and (without knowing it) passes a wolf. The wolf takes off at the instant the rabbit passes it, accelerating at a steady rate of 2.0 m/s^2. How much time elapses before the wolf is moving as fast as the rabbit? How far is the wolf from the rabbit when it reaches this speed?

Answer 1

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

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