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igtguith
28.05.2020 •
Mathematics
A second particle, Q, also moves along the x-axis so that its velocity for 0 £ £t 4 is given by Q t cos 0.063 ( ) t 2 v t( ) = 45 meters per hour. Find the time interval during which the velocity of particle Q is at least 60 meters per hour. Find the distance traveled by particle Q during the interval when the velocity of particle Q is at least 60 meters per hour.
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Ответ:
The time interval when
is at ![1.866 \leq t \leq 3.519](/tpl/images/0669/1675/86698.png)
The distance is 106.109 m
Step-by-step explanation:
The velocity of the second particle Q moving along the x-axis is :
So ; the objective here is to find the time interval and the distance traveled by particle Q during the time interval.
We are also to that :
The schematic free body graphical representation of the above illustration was attached in the file below and the point when
is at 4 is obtained in the parabolic curve.
So,
is at ![1.866 \leq t \leq 3.519](/tpl/images/0669/1675/86698.png)
Taking the integral of the time interval in order to determine the distance; we have:
distance =![\int\limits^{3.519}_{1.866} {V_Q(t)} \, dt](/tpl/images/0669/1675/57e1e.png)
=![\int\limits^{3.519}_{1.866} {45\sqrt{t} cos(0.063 \ t^2)} \, dt](/tpl/images/0669/1675/841b4.png)
= By using the Scientific calculator notation;
distance = 106.109 m
Ответ:
D
Step-by-step explanation: