Final answer:
The formula d = kt represents direct variation in mathematics, where distance is directly proportional to time. The constant k is the speed, and a straight line on a d vs. t graph indicates constant velocity.
Step-by-step explanation:
The relationship d = kt represents a form of direct variation where the distance d traveled is directly proportional to the time t. In this equation, k is the constant of proportionality and represents the rate of travel, or speed. If, for example, a car travels 150 kilometers in 3.2 hours, the average speed (Vavg) is calculated as Vavg = distance/time = 150 km / 3.2 h = 47 km/h. This demonstrates direct variation, as doubling the time of travel would also double the distance traveled, provided the speed remains constant.
In more complex scenarios involving acceleration, such as a car braking with a constant deceleration or a skydiver falling under the influence of gravity and air resistance, different kinematic equations are used. These scenarios are described by equations like d = d0 + vt for constant velocity or include acceleration terms such as 1/2 at² when a constant acceleration is involved.
A fundamental concept in physics and mathematics is that the slope of a position vs. time graph represents velocity. As such, if the plot of d versus t is a straight line, the car is moving at a constant velocity — the slope of this line.