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Eddi Din [679]
2 years ago
14

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

city from time t=0. 75 to time t=2. 25 ?
Advanced Placement (AP)
1 answer:
Firlakuza [10]2 years ago
6 0

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)

V(t) = -0.665.

Read more on acceleration here: brainly.com/question/24728358

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