Starting from a pillar, you run a distance 200 m east (the + x-direction) at an average speed of 5.0 m/s, and then run a distance 280 m west at an average speed of 4.0 m/s to a post.
Q: Calculate your average velocity from pillar to post.
Total distance = 200-280=-80
Total time = 200/5 + 280/4 seconds
= 110 seconds
Calculate the average velocity using
average velocity
= total distance / total time
Watch the sign of all quantities.
-0.727
Calculate the horizontal force required to accelerate a 20 kg grocery cart from rest to .50 m/s in 2 s.
To calculate the average velocity, we need to consider both the distance traveled and the time taken. Average velocity is a vector quantity, which means it has both magnitude and direction. In this case, the direction would be the direction from the pillar to the post.
First, let's calculate the time taken for each leg of the journey using the formula:
time = distance / speed
For the eastward leg:
distance = 200 m
speed = 5.0 m/s
time eastward = 200 m / 5.0 m/s = 40 s
For the westward leg:
distance = 280 m
speed = 4.0 m/s
time westward = 280 m / 4.0 m/s = 70 s
Now, let's calculate the average velocity using the formula:
average velocity = total displacement / total time
Displacement is the change in position and is calculated as the difference between the final position and the initial position. Since the eastward direction is considered positive, and the westward direction is considered negative:
total displacement = (displacement eastward) + (displacement westward)
displacement eastward = 200 m (positive)
displacement westward = -280 m (negative)
total displacement = 200 m - 280 m = -80 m
total time = time eastward + time westward = 40 s + 70 s = 110 s
average velocity = -80 m / 110 s
Therefore, the average velocity from the pillar to the post is approximately -0.73 m/s (rounded to two decimal places). The negative sign indicates that the velocity is in the opposite direction to the initial eastward direction.