An object moves along the x axis according to the equation x = 3.80t^2 - 2.00t +

Question

An object moves along the x axis according to the equation x = 3.80t^2 - 2.00t + 3.00, where x is in meters and t is in seconds, (a) Determine the average speed between t = 2.40 s and t = 3.50 s. Determine the instantaneous speed at t = 2.40 s. Determine the instantaneous speed at t = 3.50 s. Determine the average acceleration between t = 2.40 s and t = 3.50 s. Determine the instantaneous acceleration at t = 2.40 s. Determine the instantaneous acceleration at t = 3.50 s. At what time is the object at rest?

Explanation / Answer

a)

At T=2.40 the object was at 3.80*2.40^2 - 2* 2.40+ 3 = 20.088 m .
At T=3.50 the object was 3.80*3.50^2 - 2*3.50 + 3 = 42.55 m

So the average speed is (42.55-20.088)/(3.50-2.40) = 20.42m/s.

b)

Instantaneous speed at time t is the derivative of the location function at the point t.

x(t) = 3.80*t^2 - 2*t + 3
so v(t) = dx/dt = 7.60*t - 2
for the time t=2.40

v(t) = 7.60 * 2.40 - 2 = 16.26 m/s .

for the time t=3.50

v(t) = 7.60*3.50 - 2 = 24.6 m/s

c)

average acceleration = (24.6 - 16.26) / (3.50-2.40) = 7.581 m/s^2

d)

a(t) = dv/dt = 7.60 m/s^2 in both cases

e)

v(t) = 0

7.60 t - 2 = 0

t = 2 / 7.60 = 0.263 s

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