acceleration-time graph

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A graph that shows acceleration plotted against time for a particle moving in a straight line. Let v(t) and a(t) be the velocity and acceleration, respectively, of the particle at time t. The acceleration-time graph is the graph y=a(t), where the t-axis is horizontal and the y-axis is vertical with the positive direction upwards. With the convention that any area below the horizontal axis is negative, the area under the graph between t=t1 and t=t2 is equal to v(t2)−v(t1). (Here a common convention has been followed, in which the unit vector i in the positive direction along the line has been suppressed. The velocity and acceleration of the particle are in fact vector quantities equal to v(t)i and a(t)i, respectively.)

Subjects: Mathematics.

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