[ r(t)=(2 t+1) i+(t-4) j ] * Displacement between t_(1)=2 s and t_(2)=4 s * Average velocity between t=2 s and t=4 s * velocity at t=2 s * Acceleration at t=3 mathrm(~s)

Displacement between $t_{1}=2s$ and $t_{2}=4s$:<br />$r(4) - r(2) = [(2*4+1)i + (4-4)j] - [(2*2+1)i + (2-4)j] = (9i + 0j) - (5i + -2j) = 4i + 2j$<br /><br />Average velocity between $t=2s$ and $t=4s$:<br />$\frac{r(4) - r(2)}{4-2} = \frac{4i + 2j}{2} = 2i + j$<br /><br />Velocity at $t=2s$:<br />$r'(2) = \frac{d}{dt}[(2t+1)i + (t-4)j] = 2i + j$<br /><br />Acceleration at $t=3s$:<br />$r''(3) = \frac{d^2}{dt^2}[(2t+1)i + (t-4)j] = 0i + 0j = 0$