A fox is chasing a bunny. 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?
Well, if a fox is chasing a bunny, it sounds like they're having a real-life game of "Catch Me If You Can." The bunny seems to have some serious bunny hops.
To find the average acceleration of the bunny during this half-second interval, we need to find the change in velocity and divide it by the time taken. The initial velocity of the bunny was 7 m/s to the east, and it changed to 12 m/s to the west. So the change in velocity is 12 m/s - (-7 m/s) = 19 m/s (remember, negative West is the opposite direction of positive East).
Now that we know the change in velocity, we can divide it by the time taken, which is 0.5 seconds. Therefore, the average acceleration of the bunny is:
Average acceleration = Change in velocity / Time taken
= 19 m/s / 0.5 s
= 38 m/s²
So, the magnitude of the bunny's average acceleration is 38 m/s². However, since the bunny changed its direction from east to west, the direction of the acceleration is also changing. Let's say the bunny's initial direction was positive, so we can take the direction of the acceleration as negative. Therefore, the bunny's average acceleration during this half-second interval is 38 m/s² to the west.
Hope that brings a hop to your step!
To find the bunny's average acceleration, we need to calculate the change in velocity and divide it by the time interval. The change in velocity is the final velocity minus the initial velocity.
Given:
Initial velocity (east) = 7 m/s
Final velocity (west) = -12 m/s (negative sign indicates direction)
Time interval = 0.5 seconds
To calculate the change in velocity, we subtract the final velocity from the initial velocity:
Change in velocity = Final velocity - Initial velocity
Change in velocity = -12 m/s - 7 m/s
Change in velocity = -19 m/s
Now we can calculate the average acceleration by dividing the change in velocity by the time interval:
Average acceleration = Change in velocity / Time interval
Average acceleration = -19 m/s / 0.5 s
Average acceleration = -38 m/s²
The magnitude of the average acceleration is the absolute value of the value obtained above, which is 38 m/s². The direction of the average acceleration is negative (westward) since the velocity changed from east to west.