A particle has a constant acceleration of $\vec{a}=$ $\left(6.0 \mathrm{~m} / \mathrm{s}^2\right) \hat{i}+\left(4.0 \mathrm{~m} / \mathrm{s}^2\right) \hat{j}$. At time $t=0$, the velocity is zero and the position vector is $\vec{r}_0=(10 \mathrm{~m}) \hat{i}$.

$(b)$ Find the equation of the particle's path in the $x y$ plane and sketch the path.

At time zero, a particle is at $x=4.0 \mathrm{~m}$ and $y=3.0 \mathrm{~m}$ and has velocity $\vec{v}=(2.0 \mathrm{~m} / \mathrm{s}) \hat{i}+(-9.0 \mathrm{~m} / \mathrm{s}) \hat{j}$. The acceleration of the particle is constant and is given by $\vec{a}=\left(4.0 \mathrm{~m} / \mathrm{s}^2\right) \hat{i}+\left(3.0 \mathrm{~m} / \mathrm{s}^2\right) \hat{j}$.

$(b)$ Express the position vector at $t=4.0 \mathrm{~s}$ in terms of $\hat{i}$ and $\hat{j}$. In addition, give the magnitude and direction of the position vector at this time.

At time zero, a particle is at $x=4.0 \mathrm{~m}$ and $y=3.0 \mathrm{~m}$ and has velocity $\vec{v}=(2.0 \mathrm{~m} / \mathrm{s}) \hat{i}+(-9.0 \mathrm{~m} / \mathrm{s}) \hat{j}$. The acceleration of the particle is constant and is given by $\vec{a}=\left(4.0 \mathrm{~m} / \mathrm{s}^2\right) \hat{i}+\left(3.0 \mathrm{~m} / \mathrm{s}^2\right) \hat{j}$.

$(a)$ Find the velocity at $t=2.0$ s.

A particle moves in the $x y$ plane with constant acceleration. At time zero, the particle is at $x=$ $4 \mathrm{~m}, y=3 \mathrm{~m}$ and has velocity $\vec{v}=(2 \mathrm{~m} / \mathrm{s}) \hat{i}+(-9 \mathrm{~m} / \mathrm{s}) \hat{j}$. The acceleration is given by $\vec{a}=\left(4 \mathrm{~m} / \mathrm{s}^2\right) \hat{i}+\left(3 \mathrm{~m} / \mathrm{s}^2\right) \hat{j}$. (a) Find the velocity at $t=2 \mathrm{~s}$. (b) Find the position at $t=4 \mathrm{~s}$. Give the magnitude and direction of the position vector.

At $t=0$, a particle located at the origin has a velocity of $40 \mathrm{~m} / \mathrm{s}$ at $\theta=45^{\circ}$. At $t=3.0 \mathrm{~s}$, the particle is at $x=100 \mathrm{~m}$ and $y=80 \mathrm{~m}$ and has a velocity of $30 \mathrm{~m} / \mathrm{s}$ at $\theta=50^{\circ}$. Calculate

$(b)$ the average acceleration of the particle during this 3.0-s interval.

At $t=0$, a particle located at the origin has a velocity of $40 \mathrm{~m} / \mathrm{s}$ at $\theta=45^{\circ}$. At $t=3.0 \mathrm{~s}$, the particle is at $x=100 \mathrm{~m}$ and $y=80 \mathrm{~m}$ and has a velocity of $30 \mathrm{~m} / \mathrm{s}$ at $\theta=50^{\circ}$. Calculate

$(a)$ the average velocity.