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An object moves in a circle with constant speed. How is the acceleration vector oriented?

Under constant acceleration, what best describes the behavior of an object's velocity?

If a runner's position is constant over a period of time, which statement is true of their velocity during that same period?

A car accelerates from rest to $20 \frac{m}{s}$ in 5 seconds. What is the average acceleration of the car?

The slope of a position vs. time graph represents which quantity?

What does the area under a velocity vs. time curve represent?

Consider a position vs. time plot where the position is described by $x(t) = 3t^2 + 2t + 1$. What is the instantaneous velocity at time $t = 2$?

An object's acceleration is described by the function $a(t) = 4t$. If the object starts from rest, what is the object's velocity at $t = 3$?

A car accelerates at a constant rate of $10 rac{m}{s^2}$ on a straight track of 20 meters leading to a ravine. To clear the ravine, the car needs a minimum speed of $40 rac{m}{s}$ at the end of the track. What is the minimum initial velocity, $v_0$, required for the car to successfully clear the ravine?

Car #3 has a velocity described by the function $v_3 = \alpha t^5$, where $\alpha = 0.2 rac{m}{s^6}$. What is Car #3's acceleration, $a_3$, as a function of time?

A car is navigating an icy road that forms a quarter circle with a radius of 30 meters. If the car accelerates faster than $14 rac{km}{hour \cdot second}$, it will slide. Under these conditions, what is the shortest time the car can complete the turn without sliding?

Bob is standing on the ground observing an airplane, a balloon, and a car on a windy day. Which of the following introduces relative motion considerations?

A car starts from rest and accelerates at a constant rate of $5 m/s^2$ for a distance of 10 meters. What is the car's final velocity?

An object's velocity is given by $v(t) = 3t^2 + 2t$. What is the object's acceleration at $t = 2$ seconds?

A car moves around a circular track with a radius of 50 meters. If the car's maximum acceleration is $4 m/s^2$, what is the maximum possible speed the car can maintain without sliding off the track?

A plane is flying north at $200 m/s$ relative to the air. If there is a wind blowing east at $50 m/s$, what is the magnitude of the plane's velocity relative to the ground?

Using Bob's measurements, what is the y-component of the plane's velocity relative to Bob?

If $\vec{v}{p/B}$ represents the plane's velocity relative to Bob, and $\vec{v}{c/B}$ represents the car's velocity relative to Bob, which of the following expressions gives the plane's velocity relative to the car, $\vec{v}_{p/c}$?

What is the x-component of the plane's velocity relative to the car?

If the plane's velocity relative to the car is $\vec{v}_{p/c} = 60 \frac{m}{s}\hat{i} - 70 \frac{m}{s}\hat{j}$, what is the angle the plane's velocity makes with respect to the x-axis, according to the car?

A cannon is fired at an angle of $10^{\circ}$ with respect to the ground and is a distance $D = 50$ meters away from a wall. If the cannonball hits the wall straight on, what does this imply about the vertical component of the cannonball's velocity at the moment of impact?

A cannonball is fired at a wall 50 meters away with an angle of $10^{\circ}$. What kinematic condition must be met for the cannonball to hit the wall 'straight on'?

A cannonball is fired towards a wall. Assuming the cannonball hits the wall 'straight on', what can be inferred about the relationship between the launch angle $\theta$ and the velocity components at the time of impact?

A cannon is positioned 50 meters away from a wall that is 10 meters high. The cannonball is fired at an angle of $10^{\circ}$ relative to the ground and hits the wall 'straight on.' Which statement is most accurate?

Circular Motion Acceleration

Direction of Acceleration in Circular Motion

Velocity Formula (Constant Acceleration)

Position Formula (Constant Acceleration)

Derivative Definition

Integral Definition

Average Velocity

Average Acceleration

Cartesian Coordinate System (Navigation)

Relative velocity notation: Vp/B

Relative Velocity Formula

Equation for Plane's Velocity Relative to Car

Angle of a Vector

Formula to Find Angle from Components

Projectile Motion

Launch Angle (Projectile Motion)

Minimum Initial Velocity ($v_0$)

Instantaneous Acceleration

Acceleration Function

Maximum Velocity on a Curve

Minimum Time for a Turn

Centripetal Acceleration

Relative Velocity

Vector Notation