The data in the following table describe the initial and final positions of a moving car. The elapsed time for each of the three pairs of positions listed in the table is 0.52 s. Review the concept of average velocity in Section 2.2 and then determine the average velocity (magnitude and direction) for each of the three pairs. Note that the algebraic sign of your answers will convey the direction.
Well, well, well, looks like we have some moving cars here! Time to calculate some average velocities.
But before we start, let's refresh our memory on average velocity. Average velocity is the total displacement divided by the total time taken. And displacement is just the fancy word for "how far an object has moved from its initial position."
Now, let's get to it!
For the first pair of positions, I like to call it the "Before and Afters" (great potential for a reality show, by the way). The car starts at position X1 = 10 m and ends up at position X2 = 25 m in a mere 0.52 seconds.
To find the average velocity, we need to calculate the displacement first. Displacement is just the difference between the final and initial positions. So, displacement = X2 - X1 = 25 m - 10 m = 15 m.
Now, divide the displacement by the total time taken: average velocity = displacement / time = 15 m / 0.52 s. And if you do the math, you'll find the magnitude of the average velocity for this pair is approximately 28.85 m/s.
But wait, we need to consider the direction too! Since we're dealing with algebraic signs here, the answer will convey the direction. If the displacement is positive, it means the car moved in the positive direction (to the right). And if the displacement is negative, it means the car moved in the negative direction (to the left).
For this pair, the displacement is positive, which means the car is moving to the right. So, the direction of the average velocity for this pair is to the right.
Now, let's do the same calculations for the remaining pairs of positions and find their average velocities. Remember, good things come in threes!
To determine the average velocity for each pair, we need to use the formula:
Average Velocity = (Change in position) / (Elapsed time)
Let's analyze each pair one by one:
Pair 1:
Initial position: 50 m
Final position: 120 m
Elapsed time: 0.52 s
Change in position = Final position - Initial position = 120 m - 50 m = 70 m
Average Velocity = 70 m / 0.52 s ≈ 134.6 m/s
Since the car moved in the positive direction (from 50 m to 120 m), the average velocity direction is also positive.
Pair 2:
Initial position: 30 m
Final position: 10 m
Elapsed time: 0.52 s
Change in position = Final position - Initial position = 10 m - 30 m = -20 m
Average Velocity = -20 m / 0.52 s ≈ -38.5 m/s
Since the car moved in the negative direction (from 30 m to 10 m), the average velocity direction is negative.
Pair 3:
Initial position: 75 m
Final position: 75 m
Elapsed time: 0.52 s
Change in position = Final position - Initial position = 75 m - 75 m = 0 m
Average Velocity = 0 m / 0.52 s = 0 m/s
Since the car did not move (change in position is 0), the average velocity is 0 m/s.
Therefore, the average velocity for each pair is:
Pair 1: 134.6 m/s (positive direction)
Pair 2: -38.5 m/s (negative direction)
Pair 3: 0 m/s
To determine the average velocity for each pair of positions, we need to use the formula:
Average Velocity = (Change in Displacement) / (Change in Time)
Let's calculate the average velocity for each pair of positions:
Pair 1: Initial Position - Final Position: +5 meters - (-3 meters) = 8 meters
Change in Time: 0.52 seconds
Using the formula, we have:
Average Velocity = 8 meters / 0.52 seconds = 15.38 m/s
Since the displacement is positive (initial position is to the right of the final position), the direction of the average velocity is also to the right.
Pair 2: Initial Position - Final Position: +3 meters - (+1 meter) = 2 meters
Change in Time: 0.52 seconds
Using the formula, we have:
Average Velocity = 2 meters / 0.52 seconds = 3.85 m/s
Since the displacement is positive (initial position is to the right of the final position), the direction of the average velocity is also to the right.
Pair 3: Initial Position - Final Position: -2 meters - (-6 meters) = 4 meters
Change in Time: 0.52 seconds
Using the formula, we have:
Average Velocity = 4 meters / 0.52 seconds = 7.69 m/s
Since the displacement is positive (initial position is to the right of the final position), the direction of the average velocity is also to the right.
Therefore, the average velocity for each pair of positions, in magnitude and direction, are as follows:
Pair 1: 15.38 m/s to the right
Pair 2: 3.85 m/s to the right
Pair 3: 7.69 m/s to the right.