An object moves along the x axis according to the equation x = 2.50t^2 - 2.00t +

Question

An object moves along the x axis according to the equation x = 2.50t^2 - 2.00t + 3.00, where x is in meters and t is in seconds. (a) Determine the average speed between t = 1.90 s and t = 3.80 s. m/s (b) Determine the instantaneous speed at t = 1.90 s. m/s Determine the Instantaneous speed at t = 3.80 s. m/s (c) Determine the average acceleration between t = 1.90 t and t = 3.80 s. m/s^2 (d) Determine the instantaneous acceleration at t = 1.90 s. m/s^2 Determine the instantaneous acceleration at t = 3.80 s. m/s^2 (e) At what time is the object at rest? s

Explanation / Answer

a)

average speed = distance / time

= (2.5*(3.8^2 - 1.9^2 ) -2*(3.8 - 1.9) )/(3.8 - 1.9)

= 12.25 m/s

b)

instantaneous speed,v = dx/dt = 5*t - 2

So, at t = 1.9 s

v = 5*1.9 - 2 = 7.5 m/s

At t = 3.8 s,

v = 5*3.8 - 2 = 17 m/s

c)

average acceleration = change in velocity / time

= 5*(3.8 - 1.9)/(3.8 - 1.9)

= 5 m/s2

d)

instantaneous acceleration = dv/dt = 5 m/s2

So, at t = 1.9s, a = 5 m/s2

at t = 3.8 s, a = 5 m/s2

e)

v = 5t - 2

So, for rest , v = 0

So, t = 2/5 = 0.4 s <-----answer

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