Aparticle moves along the x-axis with velocity v(t) = t2 - 4, with t measured in seconds and v(t) measured in feet per second. find the total distance travelled by the particle from t = 0 to t = 3 seconds. (4 points)

Total distance D=7.66 ft

Explanation:  

Given that:  

Here velocity of particle will be zero at t=2 sec,so we take interval to find total distance.

We know that

       ds=V dt

So  

It means that ,the area of velocity-time(V-t) graph will give the displacement.

Given that

So now by putting the value in above integration

s= -5.33+2.33 ft

 s= -3 ft  (we know that displacement is a vector quantity so it have sing)

So this is the displacement of particle at time 0 sec to 3 sec.

To find the total distance we will add all take mode on -5.33 ft and and will add with 2.33 ft instead of subtract.

So the total distance travelled by particle D=7.66 ft.

D=7.66 ft

in simple terms, the principle states that the buoyancy force on an object is equal to the weight of the fluid displaced by the object, or the density of the fluid multiplied by the submerged volume times the gravitational acceleration, g. this is also known as upthrust.

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