Motion in One Dimension

The SI unit of displacement is the meter (m), which is the standard unit of length in the International System of Units (SI).

The magnitude of the displacement is simply the distance traveled by the object, regardless of the direction. In this case, the magnitude of the displacement is 20 meters.

The total displacement of the object is the change in its position, which is calculated by subtracting the initial position from the final position. In this case, the total displacement is 10 meters - (-5 meters) = 15 meters.

The SI unit of velocity is the meter per second (m/s), which represents the rate of change of displacement with respect to time.

Average velocity is calculated by dividing the total displacement by the time taken. In this case, the average velocity is 30 meters / 5 seconds = 6 meters per second.

Average speed is calculated by dividing the total distance traveled by the time taken. In this case, the average speed is 100 kilometers / 2 hours = 50 kilometers per hour.

The SI unit of acceleration is the meter per second squared (m/s^2), which represents the rate of change of velocity with respect to time.

Average acceleration is calculated by dividing the change in velocity by the time taken. In this case, the average acceleration is (20 m/s - 0 m/s) / 5 seconds = 4 meters per second squared.

Final velocity can be calculated using the equation v = u + at, where u is the initial velocity (0 m/s), a is the acceleration (2 m/s^2), and t is the time (10 seconds). Plugging in the values, we get v = 0 m/s + 2 m/s^2 * 10 seconds = 20 meters per second.

At the maximum height, the object's velocity becomes zero. Using the equation v^2 = u^2 + 2as, where v is the final velocity (0 m/s), u is the initial velocity (10 m/s), a is the acceleration due to gravity (-9.8 m/s^2), and s is the displacement (maximum height), we can solve for s. Plugging in the values, we get 0^2 = 10^2 + 2 * (-9.8 m/s^2) * s, which gives s = 10 meters.

Using the equation v^2 = u^2 + 2as, where v is the final velocity (unknown), u is the initial velocity (0 m/s), a is the acceleration due to gravity (-9.8 m/s^2), and s is the displacement (50 meters), we can solve for v. Plugging in the values, we get v^2 = 0^2 + 2 * (-9.8 m/s^2) * 50 meters, which gives v = 30 meters per second.

To convert kilometers per hour to miles per hour, we need to multiply by 0.621371. Therefore, the average speed in miles per hour is 200 kilometers per hour * 0.621371 = 124.2742 miles per hour, which is approximately 124 mph.

Total displacement is calculated by multiplying the velocity by the time taken. In this case, the total displacement is 10 m/s * 20 seconds = 200 meters.

Final velocity can be calculated using the equation v = u + at, where u is the initial velocity (0 m/s), a is the acceleration (2 m/s^2), and t is the time (30 seconds). Plugging in the values, we get v = 0 m/s + 2 m/s^2 * 30 seconds = 60 meters per second.