Final answer:
To calculate distance and displacement from a velocity vs. time graph, one must find the area under the graph, which is straightforward if velocity is constant. For constant acceleration, the area of the triangle between the velocity line and time axis represents displacement. Energy considerations help derive final speed in scenarios like a rock thrown from a bridge, where direction thrown does not affect the speed on impact.
Step-by-step explanation:
To calculate the distance and displacement of a truck after 15 seconds using a velocity vs. time graph, one needs to consider the area under the graph. If the graph is a straight line, the area can be interpreted as a rectangle or a triangle, depending on whether the graph shows constant velocity or constant acceleration, respectively. For constant velocity, distance and displacement will be the product of velocity and time. In the case of acceleration, the area of the triangle (half the base times the height) gives you the displacement.
For a graph showing velocity increasing from 0 to 10 m/s over a 15-second interval, we can calculate the displacement by finding the area of the triangle formed: ½ × base (time) × height (velocity), which is ½ × 15 s × 10 m/s = 75 m. Distance and displacement will be the same if the motion is in a straight line and the object doesn't change direction.
In practice problems like the rock thrown from a bridge, energy considerations are used to find the final speed. Neglecting air resistance, energy conservation tells us that the initial potential and kinetic energy will equal the kinetic energy just before impact. This applies regardless of the direction thrown because gravitational potential energy only depends on height, not the path taken.