🚨 Hurry, space in our FREE summer bootcamps is running out. 🚨Claim your spot here.

# A 5.00-kg particle starts from the origin at time zero. Its velocity as a function of time is given by $$\overrightarrow{\mathbf{v}}=\left(6 \mathrm{m} / \mathrm{s}^{3}\right) t^{2} \hat{\mathbf{i}}+\left(2 \mathrm{m} / \mathrm{s}^{2}\right) t \hat{\mathbf{j}}$$ (a) Find its position as a function of time. (b) Describe its motion qualitatively. (c) Find its acceleration as a function of time. (d) Find the net force exerted on the particle as a function of time. (e) Find the net torque about the origin exerted on the particle as a function of time. (f) Find the angular momentum of the particle as a function of time. (g) Find the kinetic energy of the particle as a function of time. (h) Find the power injected into the particle as a function of time.

## a) $2 t^{3} \hat{\mathbf{i}}+t^{2} \hat{\mathbf{j}}$b) If $\vec{r}$ and $\vec{v}$ are parallel to each other, then the particles travel in a straight line.c) $(12 t \hat{\mathbf{i}}+2 \hat{\mathbf{j}}) \mathrm{m} / \mathrm{s}^{2}$d) $60 t \hat{\mathbf{i}}+10 \hat{\mathbf{j}} \mathrm{N}$e) $\left(-40 t^{3} \mathrm{N} \cdot \mathrm{m}\right) \hat{\mathbf{k}}$f) $\left|-10 t^{4} \hat{\mathbf{k}}\right|$g) $90\left(\mathrm{m} / \mathrm{s}^{3}\right)^{2} t^{4}+10\left(\mathrm{m} / \mathrm{s}^{2}\right)^{2} t^{2}$h) $\left(300 t^{3} \mathrm{W}\right)+20 t \mathrm{W}$

#### Topics

Moment, Impulse, and Collisions

### Discussion

You must be signed in to discuss.
SR

Sihle R.

October 16, 2020

Lectures

Join Bootcamp