Question

An object moves along the x axis according to the equation x = 3.25t2 − 2.00t + 3.00, where x is in meters and t is in seconds.

(a) Determine the average speed between t = 3.30 s and t = 4.40 s. m/s

(b) Determine the instantaneous speed at t = 3.30 s. m/s Determine the instantaneous speed at t = 4.40 s. m/s

(c) Determine the average acceleration between t = 3.30 s and t = 4.40 s. m/s2

(d) Determine the instantaneous acceleration at t = 3.30 s. m/s2 Determine the instantaneous acceleration at t = 4.40 s. m/s2

(e) At what time is the object at rest? s

Answer 1

a)

at t = 3.3

x1 = 3.25* 3.3^2 - 2 * 3.3 + 3 =31.7925 m

at t = 4.4 s

x2 = 57.12 m

av speed = ( x2 - x1) / ( 4.4 - 3.3) = 23.025 m/s

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b)

differentiating both side

v = dx /dt = 6.5 t - 2

at t = 3.3 s

v1 = 6.5* 3.3 - 2 = 19.45 m/s

at t = 4.4

v2 = 6.5* 4.4 - 2 = 26.6 m/s

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c)

av acceleration = ( v2 - v1) / ( 4.4 - 3.3) = 6.5 m/s^2

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d)

instantaneous acceleration is given by

a = dv /dt = 6.5 m/s^2

at t = 3.3 s

a1 = 6.5 m/s^2

at t = 4.4 s

a2 = 6.5 m/s^2

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e)

0 = 6.5 t - 2

t = 0.3077 s

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