Answer:
calculate the force (how fast or hard it is moving) of the object
Step-by-step explanation:
4300×.30 = 1290
Her costs should be no more than $1290
The function <em>position</em> of the particle is s(t) = (1 / 12) · t⁴ + (7 / 6) · t³ + 3 · t² + (63 / 4) · t.
<h3>What are the parametric equations for the motion of a particle?</h3>
By mechanical physics we know that the function <em>velocity</em> is the integral of function <em>acceleration</em> and the function <em>position</em> is the integral of function <em>velocity</em>. Hence, we need to integrate twice to obtain the function <em>position</em> of the particle:
Velocity
v(t) = ∫ t² dt - 7 ∫ t dt + 6 ∫ dt
v(t) = (1 / 3) · t³ - (7 / 2) · t² + 6 · t + C₁
Position
s(t) = (1 / 3) ∫ t³ dt - (7 / 2) ∫ t² dt + 6 ∫ t dt + C₁ ∫ dt
s(t) = (1 / 12) · t⁴ + (7 / 6) · t³ + 3 · t² + C₁ · t + C₂
Now we find the values of the <em>integration</em> constants by solving the following system of <em>linear</em> equations:
0 = C₂
63 / 4 = C₁ + C₂
The solution of the system is C₁ = 63 / 4 and C₂ = 0. The function <em>position</em> of the particle is s(t) = (1 / 12) · t⁴ + (7 / 6) · t³ + 3 · t² + (63 / 4) · t.
To learn more on parametric equations: brainly.com/question/9056657
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