Please I will give 80 points and branilest

Advanced Placement (AP)

1 answer:

igomit [66]3 years ago

4 0

Answer:

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For time t≥0 , the acceleration of an object moving in a straight line is given by a(t)=sin(t23). what is the net change in velo

Firlakuza [10]

The net change in velocity during the given time interval is equal to -0.665.

<u>Given the following data:</u>

Initial time = 0.75 seconds.

Final time = 2.25 seconds.

Acceleration, $a(t) = sin(\frac{t^2}{3} )$

<h3>How to calculate the net change in velocity.</h3>

Since acceleration is the rate of change of velocity of an object, we would derive an expression for the velocity by differentiating with respect to time:

$V(t) = \frac{d}{dt} a(t)\\\\V(t) = \frac{d}{dt} (sin(\frac{t^2}{3} ))\\\\V(t) = cos( \frac{t^2}{3})(\frac{2t}{3})\\\\V(t) = \frac{2t}{3}cos( \frac{t^2}{3})$

Substituting the time interval, we have:

$V(t) = \frac{2\times 2.25}{3}cos( \frac{2.25^2}{3})- \frac{2\times 0.75}{3}cos( \frac{0.75^2}{3})\\\\V(t) = \frac{4.5}{3}cos( \frac{5.0625}{3})- \frac{1.5}{3}cos( \frac{0.5625}{3})\\\\V(t) =1.5(-0.11643)-0.5(0.98247)$