Velocity

Velocity is a vector quantity that not only considers the magnitude (speed) but also the direction of an object's motion. On the other hand, speed is a scalar quantity that only measures the magnitude of an object's motion. Therefore, the key distinction between speed and velocity is that velocity must have a direction associated with it, while speed does not require any specific direction.

The distance traveled by a train can be calculated by multiplying its velocity with the time it has traveled. In this case, the train has maintained a constant velocity of 16.0 meters per second for 26.0 seconds. Therefore, the distance traveled by the train can be calculated as 16.0 m/s * 26.0 s = 416 meters.

The car maintains a constant velocity of 18.0 meters per second. To calculate the distance traveled, we need to convert the time from minutes to seconds. 1.50 minutes is equal to 90 seconds (1.50 minutes x 60 seconds/minute). Then, we can use the formula distance = velocity x time. Plugging in the values, we get distance = 18.0 m/s x 90 s = 1620 meters. Therefore, the correct answer is 1620 m, 1,620 m, 1620 meters, and 1,620 meters.

The time it takes for an object to travel a certain distance can be calculated using the formula time = distance/velocity. In this case, the distance is given as 400.00 meters and the velocity is given as 12.00 meters per second. By dividing the distance by the velocity, we get 400.00/12.00 = 33.33 seconds. Therefore, it will take 33.33 seconds for the speedboat to travel 400.00 meters.

The person's velocity can be calculated by dividing the distance traveled (214 meters) by the time taken (58 seconds). This gives a velocity of approximately 3.7 meters per second.

When the airplane encounters a tailwind of 15 meters per second, it means that the wind is pushing the airplane forward with a velocity of 15 m/s. Since the airplane maintains a constant velocity of 30.0 m/s, the resultant velocity is the sum of the airplane's velocity and the velocity of the tailwind. Therefore, the new resultant velocity is 30.0 m/s + 15 m/s = 45.0 m/s.

The time it takes for the taxi to travel 2.0 kilometers can be calculated by dividing the distance by the velocity. In this case, the distance is given in kilometers, so it needs to be converted to meters by multiplying by 1000. Then, divide the distance by the velocity to get the time. In this case, 2.0 kilometers is equal to 2000 meters. Dividing 2000 meters by 19.0 meters per second gives a time of approximately 105.3 seconds.

The golf ball has a constant velocity of 21 meters per second traveling North. When it encounters a strong 12 m/s wind from the west, the wind's velocity can be considered as a vector pointing west with a magnitude of 12 m/s. To find the resultant velocity, we can use the Pythagorean theorem. The North velocity and West velocity form a right triangle, with the resultant velocity as the hypotenuse. Using the Pythagorean theorem, we can calculate the magnitude of the resultant velocity as √(21^2 + 12^2) = √(441 + 144) = √585 = 24 m/s. Therefore, the ball's new resultant velocity is 24 m/s.