Solving a Particle's Motion with Acceleration a(t) = 3at + 2b

[MelissaJL]

Homework Statement

A particle moves with an acceleration a(t)=3at+2b with a=1m/s³ and b=1m/s². Determine x(t) and v(t) such that v(1s)=4m/s and x(1s)=3m.

This is how I tried to solve it:
v(t)=∫(3at+2b)dt
v(t)=3/2at²+2bt+const
v(1s)=3/2m/s³(1s²)+2m/s²(1s)+const
4m/s=7/2m/s+const
const=1/2m/s

v(t)=3/2at²+2bt+1/2m/s

x(t)=∫(3/2at²+2bt+1/2m/s)dt
x(t)=1/2at³+bt²+1/2m/s(t)+const
x(1s)=1/2m/s³(1s³)+1m/s²(1s²)+1/2m/s(1s)+const
3m=1/2m+1m+1/2m+const
const=1m

x(t)=1/2at³+bt²+1/2m/s(t)+1m

Is this right, or where am I making errors?

 

[collinsmark]

Hello MelissaJL,

Welcome to Physics Forums!

Homework Statement

A particle moves with an acceleration a(t)=3at+2b with a=1m/s³ and b=1m/s². Determine x(t) and v(t) such that v(1s)=4m/s and x(1s)=3m.

This is how I tried to solve it:
v(t)=∫(3at+2b)dt
v(t)=3/2at²+2bt+const
v(1s)=3/2m/s³(1s²)+2m/s²(1s)+const
4m/s=7/2m/s+const
const=1/2m/s

v(t)=3/2at²+2bt+1/2m/s

x(t)=∫(3/2at²+2bt+1/2m/s)dt
x(t)=1/2at³+bt²+1/2m/s(t)+const
x(1s)=1/2m/s³(1s³)+1m/s²(1s²)+1/2m/s(1s)+const
3m=1/2m+1m+1/2m+const
const=1m

x(t)=1/2at³+bt²+1/2m/s(t)+1m

Is this right, or where am I making errors?

'Looks correct to me.