A particle is moving with the given data. Find the position of the particle.A particle is moving with the given data. Find the position of the particle. a(t) = t2 − 8t + 4,  s(0) = 0,  s(1) =...

A particle is moving with the given data. Find the position of the particle.

A particle is moving with the given data. Find the position of the particle.

a(t) = t2 − 8t + 4,  s(0) = 0,  s(1) = 20
 
s(t)=_____________?

Asked on by kitabe

1 Answer | Add Yours

jeew-m's profile pic

jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted on

`a(t) = t^2-8t+4`

The derivative of velocity function v(t) is the acceleration function.

`(dv(t))/dt = a(t)`

`dv(t) = a(t)dt`

`intdv(t) = inta(t)dt`

`v(t) = inta(t)dt`

 

`v(t) = int(t^2-8t+4)dt`

`v(t) = t^3/3-4t^2+4t+C1` where C1 is a constant.

 

The derivative of position function is the velocity function.

`(ds(t))/dt = v(t)`

`ds(t) = v(t)dt`

`intds(t) = intv(t)dt`

`s(t) = intv(t)dt`

 

`s(t) = int(t^3/3-4t^2+4t+C1)dt`

`s(t) = t^4/12-4t^3/3+2t^2+C1t+C2` where C2 is a constant.

 

`s(t) = t^4/12-4t^3/3+2t^2+C1t+C2`

It is given that;

`s(0) = 0`

 

`s(1) = 20 `

 

`0 = 0^4/12-4*0^3/3+2*0^2+C1*0+C2`

`0 = C2`

 

`20 = 1^4/12-4*1^3/3+2*1^2+C1*1+0`

`20 = 3/4+C1`

`C1 = 77/4`

 

So the position function is;

`s(t) = t^4/12-(4t^3)/3+2t^2+(77t)/4`

 

 

Sources:

We’ve answered 318,957 questions. We can answer yours, too.

Ask a question