Using the following position vs. time graph, determine the total distance traveled between points B and D.

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Question

Using the following position vs. time graph, determine the total distance traveled between points B and D.

d
=
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c
m

BlackTom AI · Accepted Answer

We start by clearly identifying what is being asked: determine the total distance traveled between points B and D using the given velocity vs. time graph. Since distance is the integral of speed (absolute value of velocity) with respect to time over the interval from t_B to t_D, we will compute the area under the velocity curve from B to D.

First, locate B and D on the graph. Point B occurs at the end of the rising segment where velocity is positive (above the time axis), and point D lies later along the same segment where the velocity is still positive before it crosses toward zero or negative values. The interval from B to D spans several seconds during which velocity remains positive, so the distance traveled equals the positive area under the curve between these times.

Next, determine the velocities and time bounds for the portion from B to D. If B is at t_B ≈ 25 s with v_B ≈ 3 m/s, and D is at t_D ≈ 60 s where the velocity has decreased to 0 m/s (the zero-crossing point on the graph), then the interval length is Δt = t_D − t_B ≈ 60 − 25 = 35 s, and the velocity changes linearly from about 3 m/s down to 0 m/s over that interval.

Compute the area under a linearly decreasing velocity from 3 m/s to 0 m/s over 35 s. This area is a triangle with base Δt = 35 s and height v_B = 3 m/s, so the area (distance) is (1/2) × base × height = 0.5 × 35 × 3 = 52.5 m.

If the problem asks for distance in centimeters rather than meters, convert 52.5 m to centimeters by multiplying by 100, giving 5250 cm. Depending on how the graph is scaled or if the exact coordinates differ slightly (e.g., t_B or t_D not exactly 25 s or 60 s), the numerical result may vary slightly; the key idea is that the distance between B and D equals the positive area under the velocity-time curve over that interval.

In summary, the distance traveled from B to D is found by integrating the positive velocity from t_B to t_D, which, based on the approximate coordinates read from the graph, yields about 52.5 meters (or 5250 centimeters) of travel.

Using the following position vs. time graph, determine the total distance traveled between points B and D. d = _ _ _ _ _ _ c m

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