`a(t)=t^2-4t+6`
`a(t)=v'(t)`
`v(t)=inta(t)dt`
`v(t)=int(t^2-4t+6)dt`
`v(t)=t^3/3-4(t^2/2)+6t+c_1`
`v(t)=t^3/3-2t^2+6t+c_1`
`s(t)=intv(t)dt`
`s(t)=int(t^3/3)-2t^2+6t+c_1)dt`
`s(t)=(1/3)(t^4/4)-2t^3/3+6t^2/2+c_1t+c_2`
`s(t)=t^4/12-(2t^3)/3+3t^2+c_1t+c_2`
Let's find constants c_1 and c_2 . given s(0)=0 and s(1)=20
`s(0)=0=c_2`
`s(1)=20=1/12-2/3+3+c_1`
`20=(1-8+36)/12+c_1`
`20=29/12+c_1`
`c_1=20-29/12=211/12`
`s(t)=t^4/12-2t^3/3+3t^2+211/12t`
We’ll help your grades soar
Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.
- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support
Already a member? Log in here.
Are you a teacher? Sign up now