constant speed
The train's distance from the station is determined by the time it moves at [constant speed|constant speed] and its initial distance from the station.
Definition
The train's distance from the station is determined by the time it moves at constant speed and its initial distance from the station. This relationship is expressed as a function of time and the constant speed. The formula accounts for both the original distance and the additional distance covered during constant speed motion.
Mechanism
A skateboarder riding on a level surface maintains constant speed while throwing a ball. The ball's height follows the equation y ( t ) = − 16 t 2 + 10 t + 5. Both scenarios involve consistent velocity without acceleration. The car travels at 50 miles per hour, matching the skateboarder's 9 ft/s speed. constant speed ensures uniform motion in these examples.
Causes
constant speed A car travels at a constant speed of 50 miles per hour. The constant speed is maintained by consistent engine performance. The speed remains unchanged over time.
Examples
constant speed In the train example, the graph shows the y-intercept at (0, 250), which corresponds to the train's initial distance from the station. This point represents the starting position before the train moves at a constant speed. The intercept is linked to the distance measurement when motion begins at a steady rate.
Level Surface Mechanism
constant speed on a level surface maintains uniform horizontal motion without acceleration. The ball's vertical motion follows y(t) = −16t² + 10t + 5, governed by gravity and initial velocity. The level surface ensures no external forces alter the ball's trajectory during flight.
Time Function
The time function for constant speed represents the mathematical model of motion at uniform speed. It calculates the train's distance from the station over time by adding the original distance to the product of time and constant speed. This function accounts for both the initial position and the constant velocity of the train.
Train Distance
The train's distance from the station at constant speed is determined by multiplying the constant speed by the time traveled, then adding the initial distance. This formula shows how distance changes with time at a constant speed.