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What is the quantity which is measured by the area occupied below the velocity - time graph?
Wiki User
∙ 10y ago
Distance travelled (displacement). Distance = velocity/time, so velocity * time = distance. Likewise, x = dv/dt so the integral of velocity with respect to time (area under the graph) is x, the distance travelled.
Wiki User
∙ 10y ago
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What is the quantity which is measured by the area occupied below the velocity time graph?
If you're graphing velocity vs. time, you're denoting what velocity you're moving at various points in time. The slope of the line at any given point is your acceleration at that time. The area beneath the graph would be the total distance traveled. For example, if you were traveling at 50mph for one hour, the graph would be a straight line parallel to the x axis. The area will be 1 hour * 50 miles per hour = 50 miles. By the way, if you can get this concept down, you've figured out the basic ideas of differential and integral calculus! The slope of the graph is the differential, and the area under the curve is the integral.
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How can average velocity be zero if traveled 100m?
This question revolves around the idea of vector quantities. Vector quantities involve two factors: magnitude and direction. Velocity (as well as average velocity) is a vector quantity. The given value of 100m is a magnitude of a distance which is a scalar quantity. Average velocity can be represented as below (all V's represent velocity, not speed). Vavg = ½ (Vi + Vf ). Let us say that an object was traveling at an initial velocity of 15m/s [East] for a certain amount of time. Afterward, the object suddenly travels at a final velocity of 15m/s [West] for a certain amount of time. In total, the object may have traveled 100m. Because the direction of the two velocities are opposite, the magnitude of the two values are opposite of one another. In other words, Vavg = ½ (0m/s) = 0. Therefore, it is important to always think about the direction an object is travellng when a vector quantity is involved.
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