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An object moves along the x axis according to the equation x = 3.40 t 2 ? 2.00 t

ID: 1274776 • Letter: A

Question

An object moves along the x axis according to the equation

x = 3.40t2 ? 2.00t + 3.00,

where x is in meters and t is in seconds.

(a) Determine the average speed between t = 3.50 s and t = 4.60 s.
?m/s

(b) Determine the instantaneous speed at t = 3.50 s.
?m/s

Determine the instantaneous speed at t = 4.60 s.
?m/s

(c) Determine the average acceleration between t = 3.50 s and t = 4.60 s.
?m/s2

(d) Determine the instantaneous acceleration at t = 3.50 s.
?m/s2

Determine the instantaneous acceleration at t = 4.60 s.
?m/s2

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

Explanation / Answer

a) x(t) = 3.40t2 - 2.00t + 3.00

x(3.5) = 37.65

x(4.6) = 65.74

vave = delta x / delta t

= (65.74 - 37.65) / (4.6 - 3.5)

= 25.54 m/s

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b) v = dx / dt = 6.8t - 2

v(3.5) = 21.8 m/s

v(4.6) = 29.28 m/s

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c) a = delta v / delta t

= (29.28 - 21.8) / (4.6 - 3.5)

= 6.8 m/s

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d) a = dv / dt

a = 6.8 m/s

a(3.5) = 6.8 m/s2

a(4.6) = 6.8 m/s2