The object travelled a distance of 105 meters from time = 0 to time = 15 s. Based on the nearest options, the closest to 105 m would be option C, 90 m
To determine how far the object traveled from time = 0 to time = 15 s, we can analyze the velocity-time graph in the image provided. The area under the velocity-time graph gives the displacement of the object for the given time interval.
The graph shows a straight line decreasing from a positive velocity at time = 0 to a velocity of 0 m/s at time = 15 s. This indicates a uniformly decelerating motion. The initial velocity (vi) can be read from the graph where time = 0, and the final velocity (vf) is 0 m/s at time = 15 s. The shape of the area under the graph from time = 0 to time = 15 s is a right triangle.
The formula to calculate the area of a triangle is
, where the base is the time interval and the height is the initial velocity.
Let's calculate the displacement using the information available:
1. Determine the initial velocity (vi) from the graph at time = 0.
2. Use the formula for the area of a triangle to find the displacement (s).
Since the velocity decreases to 0 m/s linearly, the average velocity (v_avg) over this period can be calculated as
. However, since vf = 0 m/s, the v_avg will simply be
The displacement can then be calculated using the formula:
We can follow these steps to calculate the displacement as soon as we determine the initial velocity from the graph. Let's proceed with that.
The object travelled a distance of 105 meters from time = 0 to time = 15 s. However, since this option is not available in the choices provided (A. 120 m, B. 180 m, C. 90 m, D. 45 m), it's possible that there has been an estimation error due to the graphical nature of the question.