8. A person starts at a position of 25 meters and finishes at a position of 2 meters. The trip takes
4.5 seconds. What is the person's average velocity? What is the person’s average speed?
9. A person starts at a position of 2 meters and finishes at a position of 25 meters. The trip takes
4.5 seconds. What is the person's average velocity? What is the person’s average speed?
10. A train travels at a speed of 30 m/s. The train starts at an initial position of 1000 meters and
travels for 30 seconds. What is its final position?
11. At a time of 30 seconds a runner passes a distance marker labeled "125 meters." If the
velocity of the runner is +5.0 m/s, when did the runner pass the distance marker for 75
meters?
8. Wow, that person must be the world champion in walking backward! Their average velocity can be calculated by dividing the change in position (from 25 meters to 2 meters) by the time taken (4.5 seconds). As for average speed, it can be calculated by dividing the total distance traveled (23 meters) by the time taken (4.5 seconds).
9. Now that's more like it! This person seems to be running in the right direction. To find the average velocity, you divide the change in position (from 2 meters to 25 meters) by the time taken (4.5 seconds). To calculate the average speed, you divide the total distance traveled (23 meters) by the time taken (4.5 seconds).
10. Choo choo! That train is on the move. To find its final position, you multiply its speed (30 m/s) by the time taken (30 seconds) and add it to the initial position (1000 meters). All aboard for some mathematical fun!
11. Ah, a speedy runner! If the runner passed the 125-meter marker at 30 seconds with a velocity of +5.0 m/s, we can calculate when they passed the 75-meter marker. Since velocity is constant, we can use the equation v = d/t, where v is the velocity, d is the distance, and t is the time. Rearranging the equation gives us t = d/v. Plug in the numbers and let the calculations begin!
8. To find average velocity, we need to calculate the displacement and divide it by the time taken.
Displacement = Final position - Initial position = 2 meters - 25 meters = -23 meters
Average velocity = Displacement / Time = -23 meters / 4.5 seconds = -5.11 m/s
To find average speed, we need to calculate the total distance traveled and divide it by the time taken.
Total distance = Initial position - Final position = 25 meters - 2 meters = 23 meters
Average speed = Total distance / Time = 23 meters / 4.5 seconds = 5.11 m/s
9. Similar to the previous question, to find average velocity, we need to calculate the displacement and divide it by the time taken.
Displacement = Final position - Initial position = 25 meters - 2 meters = 23 meters
Average velocity = Displacement / Time = 23 meters / 4.5 seconds = 5.11 m/s
To find the average speed, we need to calculate the total distance traveled and divide it by the time taken.
Total distance = Final position - Initial position = 25 meters - 2 meters = 23 meters
Average speed = Total distance / Time = 23 meters / 4.5 seconds = 5.11 m/s
10. To find the final position, we can use the formula: Final position = Initial position + (Speed × Time)
Final position = 1000 meters + (30 m/s × 30 seconds) = 1000 meters + 900 meters = 1900 meters
So, the train's final position is 1900 meters.
11. The time it took the runner to reach the 125 meter marker can be found by dividing the distance by the velocity:
Time = Distance / Velocity = 125 meters / 5.0 m/s = 25 seconds
So, the runner passed the 75 meter marker at 25 seconds.
8. To find the person's average velocity, you need to calculate the displacement and divide it by the time taken. Displacement is the difference between the final position and the initial position. In this case, the displacement is 2 meters - 25 meters = -23 meters (negative sign indicates direction). The time taken is 4.5 seconds. Average velocity is then calculated as displacement/time = -23 meters / 4.5 seconds = -5.11 m/s (rounded to two decimal places).
To find the person's average speed, you need to calculate the total distance traveled and divide it by the time taken. Distance is the sum of the initial position and absolute value of the displacement. In this case, the distance is 25 meters + 23 meters = 48 meters. Average speed is then calculated as distance/time = 48 meters / 4.5 seconds = 10.67 m/s (rounded to two decimal places).
9. Similar to the previous question, the calculation is done by finding the displacement and dividing it by the time taken. The displacement is 25 meters - 2 meters = 23 meters. The time taken is 4.5 seconds. Average velocity is calculated as displacement/time = 23 meters / 4.5 seconds = 5.11 m/s (rounded to two decimal places).
Average speed is calculated by dividing the total distance traveled by the time taken. The distance is 2 meters + 23 meters = 25 meters. Average speed is then calculated as distance/time = 25 meters / 4.5 seconds = 5.56 m/s (rounded to two decimal places).
10. To find the final position of the train, you need to calculate the displacement using the formula displacement = initial position + (velocity x time). In this case, the initial position is 1000 meters, the velocity is 30 m/s, and the time is 30 seconds. The displacement is then calculated as 1000 meters + (30 m/s x 30 seconds) = 1900 meters.
Therefore, the train's final position is 1900 meters.
11. To find out when the runner passed the distance marker for 75 meters, you can use the equation of motion: displacement = initial position + (velocity x time). The initial position is 0 meters (since it is a marker), the displacement is 75 meters, the velocity is +5.0 m/s, and the time is unknown.
Rearranging the equation, we get time = (displacement - initial position) / velocity. Plugging in the values, we have time = (75 meters - 0 meters) / 5.0 m/s = 15 seconds.
Therefore, the runner passed the distance marker for 75 meters at 15 seconds.
#8,9) speed is distance/time, so (25-2)m/4.5s = ____ m/s
The velocity also has a sign, depending on whether the distance decreased or increased
#10) since distance = speed * time, that would be 1000 + 30*30 = ____ m
#11) 30 + (125-75)/5 = ___s
This sounds like positive direction is toward the finish line, so the markers are decreasing.