Question

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 ?

Answer 1

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

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:

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

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