A car moves in a straight line along a paved road. The velocity of the car versus time is shown: What is the distance travelled by the car from 0 s to 15 s?

Question

A car moves in a straight line along a paved road.  The velocity of the car versus time is shown:  What is the distance travelled by the car from 0 s to 15 s?

Quizplus · Accepted Answer

11ecba2d_1304_5c08_a3bf_c1d66bbb649e_MD0008_00 Although the relationships between translational variables can be expressed through several equations, graphs may also be used to explore these relationships visually. For example, a graph of velocity v versus time t plots the velocity of an object as a function of time. The area under the curve of a velocity (y-axis) vs. time (x-axis) graph is equal to the displacement of an object over the corresponding period of time. Provided that the plot of the velocity vs. time graph remains above the x-axis, this displacement is equal to the total distance traveled. The equation for displacement Δx of the object, in which x_i is the initial position and x_f is the final position, is given as: 11ecba2d_1304_5c09_a3bf_9520aec683dd_MD0008_00 The v · t component of the equation shows that the displacement Δx of a moving object is equal to the product of both axes (velocity and time) on the graph, which is equivalent to the area under the curve of this graph. In this scenario, the given graph shows that the car initially moved at a constant velocity (flat slope segment), then accelerated at a constant rate (positive slope segment), after which it maintained a new constant velocity. The area under the curve can be calculated by visualizing the area into simple geometric shapes, in this case through the form of a rectangle and a triangle. Accordingly, adding the areas of these two shapes yields total displacement: 11ecba2d_1304_5c0a_a3bf_e75281d1891b_MD0008_00 Based on these calculations, it can be concluded that the car traveled 400 m (Choice B) in the first 15 s of the journey. Educational objective: In a graph of velocity versus time, the displacement of a moving object over an interval of time can be derived from the graph by calculating the total area under the curve during that interval.

A Car Moves in a Straight Line Along a Paved