AP Physics 1 Unit 1: Kinematics

An object moves along the x-axis with the position function $x(t)=3t^2-12t+5$ (meters, with $t$ in seconds). At what time does the object momentarily come to rest?

Two students compare their commutes. Student X drives the first half of the distance at $30\text{m/s}$ and the second half at $60\text{m/s}$. Student Y drives the first half of the time at $30\text{m/s}$ and the second half of the time at $60\text{m/s}$. Which student has the larger average speed for the trip?

A stone is dropped from a tall cliff. Ignoring air resistance and taking $g=10{\text{m/s}}^2$, how far does it fall during the third second of its fall (between $t=2\text{s}$ and $t=3\text{s}$)?

A car traveling at $20\text{m/s}$ brakes uniformly and stops in $4.0\text{s}$. What is the magnitude of its acceleration?

The velocity-vs-time graph of a moving object is a straight line that starts at $v=-4\text{m/s}$ at $t=0$ and reaches $v=+6\text{m/s}$ at $t=5\text{s}$. What is the average acceleration over this interval?

A ball is thrown straight up with an initial speed of $15\text{m/s}$. Taking $g=10{\text{m/s}}^2$ and ignoring air resistance, what is the maximum height reached above the launch point?

A car accelerates uniformly from rest. After traveling $20\text{m}$, its speed is $10\text{m/s}$. What is its speed after it has traveled an additional $60\text{m}$ (i.e., $80\text{m}$ total)?

Two students start from the same point. Student A runs at a constant $4.0\text{m/s}$. Student B starts from rest at the same instant and accelerates uniformly at $2.0{\text{m/s}}^2$. How long after the start does Student B catch up with Student A?

A projectile is launched from ground level at a speed of $30\text{m/s}$ at an angle of $30°$ above the horizontal. Taking $g=10{\text{m/s}}^2$ and ignoring air resistance, how long is the projectile in the air before returning to the ground?

An object's position as a function of time is shown in a graph (not reproduced here): position is constant at $x=4\text{m}$ for $0\le t<2\text{s}$, then increases linearly to $x=10\text{m}$ at $t=5\text{s}$, then decreases linearly back to $x=4\text{m}$ at $t=8\text{s}$. What is the object's average velocity over the interval from $t=0$ to $t=8\text{s}$?