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A particle moves along a straight line such that its speed is () = 2 − + 6, where t is the time measured in seconds and the speed is measured in meters per second. a) Calculate the distance traveled between the seconds t=1 and t=3.

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onyebuchinnaji

The distance traveled by the particle between the seconds t=1 and t=3 is 14 m.

Distance traveled by the particle

The distance traveled by the particle is determined from the model of the particle's motion.

x(t) = t² - 6t

Distance traveled when t = 1

x(1) = (1)² - 6(1) = - 5 m

Distance traveled when t = 3

x(3) = (3)² - 6(3) = -9 m

Total distance traveled by t = 1 and t = 3

D = - 5 m - 9 m = - 14 m

|D| = 14 m

Thus, the distance traveled by the particle between the seconds t=1 and t=3 is 14 m.

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