A particle has acceleration at time $t$ given by $\mathbf{a} = 3t\mathbf{i} - 2\mathbf{j}$. Initially, it has a velocity given by $\mathbf{v} = \mathbf{i} + \mathbf{j}$ and a position vector of $\mathbf{r} = 4\mathbf{i} - \mathbf{j}$.
Find the velocity of the particle at $t = 2$.
Find the position vector of the particle at $t = 2$.
$7\mathbf{i} - 3\mathbf{j}$
$10\mathbf{i} - 3\mathbf{j}$
Q2
Answer
A curve $C$ has equation given by $x^2 + 2xy - 5y = 4$. Find the two points on the curve where the gradient is zero.
$(1,-1)$ and $(4,-4)$
Q3
Answer
Solve $\cos^2 x + \sin x = 1$ in the range $0 < x \leq 2\pi$.