Originally Posted by

**Soroban** Hello, rcmango!

We will integrate twice, and use the initial conditions to evaluate the constants.

Velocity is the integral of the acceleration: .**v**(t) .= .∫ **a**(t) dt

. . **v**(t) .= .∫ (24t²**i** - 12t**j**) dt .= .8t³**i** - 6t²**j** + C1

Since **v**(0) = **i** - **j**: .8·0³**i** - 6·0²**j** + C1 .= .**i** - **j** . → . C1 .= .**i** - **j**

. . Hence: .**v**(t) .= .8t³**i** - 6t²**j** + **i** - **j** . → . **v**(t) .= .(8t³ - 1)**i** - (6t² + 1)**j**

Position is the integral of velocity: .**r**(t) .= .∫ **v**(t) dt

. . **r**(t) .= .∫ [(8t³ - 1)**i** - (6t² + 1)**j**] dt .= .(2t^4 - t)**i** - (2t³ + t)**j** + C2

Since **r**(0) = **i**: .(2·0^4 - 0)**i** - (2·0³ + 0)**j** + C2 .= .**i** . → . C2 = **i**

. . Hence: .**r**(t) .= .(2t^4 - t)**i** - (2t³ + t)**j** + **i**

Therefore: .**r**(t) .= .(2t^4 - t + 1)**i** - (2t³ + t)**j**

Hmmm, too slow once again . . .