The bunny is initially hopping east at 7 m/s when it first sees the fox. Over the next half second the bunny changes its velocity to west at 12 m/s and escapes. What was the bunny's average acceleration (magnitude and direction) during this half-second interval?
If velocity and acceleration are considered positive in the east direction,
DeltaV = [-12 -7] = -19 m/s
acceleration = DeltaV/t = -19/(1/2)
= -38 m/s^2
Magnitude = 38 m/s^2, direction = west
To find the bunny's average acceleration during the half-second interval, we can use the formula:
Acceleration (a) = (Change in Velocity) / (Time)
First, we need to calculate the change in velocity. The bunny initially hops east at a velocity of 7 m/s, and then changes its velocity to west at 12 m/s.
Change in velocity = Final velocity - Initial velocity
= (-12 m/s) - (7 m/s)
= -19 m/s
Now, we need to calculate the time interval. We are given that the bunny changes its velocity over the next half second. Therefore, the time interval (t) is 0.5 seconds.
Using the formula for average acceleration, we can substitute the values:
Acceleration = (-19 m/s) / (0.5 s)
= -38 m/s^2
The magnitude of acceleration is always positive, so the magnitude of the bunny's average acceleration is 38 m/s^2. However, since the bunny changed its direction from east to west, the direction of the average acceleration is negative or in the opposite direction to its initial velocity. So, the bunny's average acceleration is -38 m/s^2, westward.
To find the bunny's average acceleration, we need to calculate the change in velocity and divide it by the time interval.
First, let's calculate the change in velocity:
Change in velocity = final velocity - initial velocity
Change in velocity = (-12 m/s) - (7 m/s)
Change in velocity = -19 m/s
Next, let's calculate the time interval:
Time interval = 0.5 seconds
Now, let's calculate the average acceleration:
Average acceleration = Change in velocity / Time interval
Average acceleration = -19 m/s / 0.5 s
Average acceleration = -38 m/s^2
Therefore, the bunny's average acceleration during this half-second interval is 38 m/s^2 to the west.