Answered

At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Discover a wealth of knowledge from experts across different disciplines on our comprehensive Q&A platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

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 velocity from time t=0. 75 to time t=2. 25 ?

Sagot :

Lanuel

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

Given the following data:

  • Initial time = 0.75 seconds.
  • Final time = 2.25 seconds.
  • Acceleration, [tex]a(t) = sin(\frac{t^2}{3} )[/tex]

How to calculate the net change in velocity.

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:

[tex]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})[/tex]

Substituting the time interval, we have:

[tex]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)[/tex]

V(t) = -0.665.

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

Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.