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12345 [234]
3 years ago
12

The function ​v(t)equals=t cubed minus 10 t squared plus 21 tt3−10t2+21t​, ​[0,99​], is the velocity in​ m/sec of a particle mov

ing along the​ x-axis. Complete parts​ (a) through​ (c). a. Determine when the motion is in the positive direction and when it is in the negative direction. b. Find the displacement over the given interval. c. Find the distance traveled over the given interval.
Physics
1 answer:
stellarik [79]3 years ago
3 0

NOTE: <em>I suppose there was an error when typing the Interval. </em>

<em>Graphing the graph up to 99 for example for point A, implies a 10-fold perioricity and for point B almost 10 integrals! That is a little expensive!</em>

<em>Which implies an extremely costly graph to count the positive and negative points. </em>

<em> I will start by performing the procedure for a shorter interval, in case it is necessary and implicit </em>

<em>Extensive interval, I think the procedure is contingent and it is simply a matter of extrapolating it. </em>

 

So things,

The function:

v (t) = t ^ 3 - 10t ^ 2 + 21t, [0.9]

a) t \in (0.3) \Rightarrow Positive address & t \in (7.9)

t \in (3.7) \Rightarrow Negative address

b) Displacement = \int \limit ^ 9_0 (t ^ 3-10 ^ t2 + 21) dt = \frac {t ^ 4} {4} - \frac {10 ^ 3} {3} + \frac {21t^2} {2} \Big| _0 ^ 9

Displacement = 60.75m

c) Distance = \int \limit ^ 0_3 (t ^ 3-19t ^ 2 + 21t) dt + \int \limit ^ 7_3 (-t ^ 3 + 10t ^ 2-21t) dt + \int \limit ^ 9_7 (t ^ 3-19t ^ 2 + 21t) dt

Distance = 167.41m

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The acceleration of the crate after it begins to move is 0.5 m/s²

We'll begin by calculating the the frictional force

Mass (m) = 50 Kg

Coefficient of kinetic friction (μ) = 0.15

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Normal reaction (N) = mg = 50 × 10 = 500 N

<h3>Frictional force (Fբ) =?</h3>

Fբ = μN

Fբ = 0.15 × 500

<h3>Fբ = 75 N</h3>

  • Next, we shall determine the net force acting on the crate

Frictional force (Fբ) = 75 N

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  • Finally, we shall determine the acceleration of the crate

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