# An object's two dimensional velocity is given by v(t) = ( 5t-t^3 , 3t^2-2t). What is the object's rate and direction of acceleration at t=5 ?

Mar 3, 2017

$a \left(5\right) = - 70 \hat{i} + 28 \hat{j}$

#### Explanation:

$v \left(t\right) = 5 t - {t}^{3} \hat{i} + 3 {t}^{2} - 2 t \hat{j}$

$a \left(t\right) = \frac{\mathrm{dv}}{\mathrm{dt}}$

$a \left(t\right) = 5 - 3 {t}^{2} \hat{i} + 6 t - 2 \hat{j}$

$a \left(5\right) = 5 - 3 \times {5}^{2} \hat{i} + 6 \times 5 - 2 \hat{j}$

$a \left(5\right) = 5 - 75 \hat{i} + 30 - 2 \hat{j}$

$a \left(5\right) = - 70 \hat{i} + 28 \hat{j}$

Here, $\hat{i}$ denotes $x$ direction and $\hat{j}$ denotes $y$ direction.