The magnitude of the total displacement of her trip is 2.2 miles.
<h3>
Total displacement of Olivia's trip</h3>
The magnitude of the total displacement of her trip is calculated as follows;
Total east journey = 0.8 mi + 1.2 mi = 2 mi
Resultant displacement = √(y² + x²)
Resultant displacement = √(0.9² + 2²)
Resultant displacement = 2.2 mi
Thus, the magnitude of the total displacement of her trip is 2.2 miles.
Learn more about displacement here: brainly.com/question/321442
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<span>a) write a polynomial expression for the position of the particle at any time t greater or equal to zero.
</span>Position is found by integrating velocity:
<span>s(t) = (t^3)/3 - 4t^2 + 7t + c
</span>where c is a constant corresponding to the position at t=0. <span>
b) at what time(s) is the particle changing direction
</span>the particle changes direction whenever the velocity is zero; the velocity function equals
<span>(t-1)(t-7) a difference of squares so the zeros are 1 and 7, it changes direction at 1 second and 7 seconds. </span><span>
c) find the total distance traveled by the particle from t=0 and t=4
</span><span>s(0) = c
s(1) = 8/3 + c
s(4) = 64/3 - 64 + 28 + c.
</span>
from 0 to 1 the particle travels 8/3 units. From 1 to 4 it travels -(64/3 - 36 - 8/3) = (-(56/3 - 108/3))
<span>=-(-52/3) = 52/3 units
</span>
<span>so in total it travels 52/3 + 8/3 =20 units</span>
