The position of a particle moving along the x-axis is given by the equation $x(t) = 3t^2 - 4t + 2$, where $x$ is in meters and $t$ is in seconds. Find the instantaneous velocity of the particle at $t = 2 \text{ s}$.

A drone's velocity in the y-direction is given by $v_y(t) = 4t^3 - 2t \text{ m/s}$. Determine its acceleration at $t = 1.5 \text{ s}$.

An object starts from rest at the origin ($x=0, t=0$). Its acceleration is given by $a(t) = 6t \text{ m/s}^2$. Find its position at $t = 3 \text{ s}$.

A car is traveling at $30 \text{ m/s}$ when the driver sees a hazard and slams on the brakes. The car decelerates at a constant rate of $5 \text{ m/s}^2$. How far does the car travel before coming to a complete stop?

A train accelerates uniformly from $15 \text{ m/s}$ to $35 \text{ m/s}$ over a distance of $500 \text{ m}$. Calculate the time it takes to cover this distance.

A person is running at a constant speed of $6 \text{ m/s}$ to catch a bus. When the person is $20 \text{ m}$ behind the bus doors, the bus starts pulling away from the stop with a constant acceleration of $1 \text{ m/s}^2$. Does the person catch the bus? If so, how long does it take?

A rock is dropped from a $45 \text{ m}$ high cliff. How long does it take to hit the ground? (Use $g = 9.8 \text{ m/s}^2$)

A ball is thrown straight up with an initial speed of $15 \text{ m/s}$. What is the maximum height it reaches?

A coin is thrown vertically downwards from a balloon at an altitude of $300 \text{ m}$ with an initial speed of $10 \text{ m/s}$. What is its velocity just before hitting the ground?

A rock is thrown horizontally off a $20 \text{ m}$ high cliff at a speed of $15 \text{ m/s}$. How far from the base of the cliff does it land?

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A football is kicked at an angle of $40^\circ$ to the horizontal with an initial speed of $25 \text{ m/s}$. Assuming level ground, calculate its horizontal range.

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A cannon fires a shell at $50 \text{ m/s}$ and $30^\circ$ above the horizontal. A target lies $40 \text{ m}$ above the cannon's launch level. Determine whether the projectile can reach that elevation. If it can, find the horizontal distance to the target.

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A passenger is walking at $1.5 \text{ m/s}$ relative to a moving walkway in an airport. The walkway itself is moving at $2.0 \text{ m/s}$ relative to the ground. What is the passenger's velocity relative to a stationary observer on the ground?

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A boat heading due North crosses a river with a velocity of $4 \text{ m/s}$ relative to the water. The river flows due East at $3 \text{ m/s}$. What is the boat's resultant velocity relative to the riverbank?

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Car A is traveling East at $20 \text{ m/s}$. Car B is traveling North at $15 \text{ m/s}$. Find the velocity of Car A relative to Car B ($\vec{v}_{AB}$).

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