AP Physics C: Mechanics Unit 1: Kinematics

The velocity of a particle is $v(t)=t^2-4t+3$ m/s. What is the total distance traveled from $t=0$ to $t=4$ s?

(Hint: factor $v$ and identify where it changes sign.)

A car decelerates uniformly from $30$ m/s to rest in $5$ s. What is the magnitude of deceleration and the stopping distance?

The velocity of a particle is $v(t)=e^{-t}$ m/s for $t\ge 0$. What is the total distance traveled from $t=0$ to $t\to \infty$?

Given $a(t)=6t$ m/s² with $v(0)=0$ and $x(0)=2$ m, find $x(3)$.

A particle moves along the $x$-axis with velocity $v(t)=3t^2-6t$ m/s. What is the acceleration at $t=2$ s?

A particle starts from rest at the origin and accelerates with $a(t)=4t$ m/s². What is the velocity at $t=3$ s?

A particle has position $\mathbf{r}(t)=t^2\hat{i}+2t^3\hat{j}$ m. What is $|\mathbf{a}|$ at $t=1$ s?

A ball is launched horizontally from a cliff 80 m high with speed $20$ m/s. Using $g=10$ m/s², how far from the base of the cliff does it land?

A particle's position is $x(t)=A\sin (\omega t)$. Using calculus, find $a(t)$ and identify the relationship between $a$ and $x$.

A particle's position is $x(t)=t^3-3t^2+2$ m. At what time(s) is the particle momentarily at rest for $t\ge 0$?

A projectile is launched at angle $\theta$ above the horizontal with initial speed $v_0$. Which expression gives the maximum height?

A particle's position components are $x(t)=v_{0x}t$ and $y(t)=v_{0y}t-\frac{1}{2}g{t}^2$. Which expression correctly gives $y$ as a function of $x$ (the trajectory equation)?