A particle starts at the origin and moves along a straight line with velocity

The velocity of a particle is

The displacement of a particle from an origin is

where $s$ is measured in metres.

A particle moves along a straight line with velocity

where $t$ is measured in seconds and $v(t)$ is measured in $\text{m s}^{-1}$; the polynomial uses the numerical value of $t$, and $k$ is a dimensionless constant. The particle changes direction at $t=1$.

The displacement of a buoy moving vertically is modelled by

where $s$ is measured in metres and $t$ in seconds.

A train moves along a straight track. Its acceleration $a\ \text{m s}^{-2}$ depends on its displacement $s\ \text{m}$ according to

When $s=0$, its speed is $6\ \text{m s}^{-1}$ and it is moving in the positive direction.

A particle moves along a straight line with velocity

Here, $t$ is measured in seconds and $v(t)$ is measured in $\text{m s}^{-1}$.

A shuttle moves along a straight track. Its velocity at time $t$ seconds is given by

where velocity is measured in $\text{m s}^{-1}$. Initially, the shuttle is $3$ metres from an origin $O$. Take the positive direction to be away from $O$, and let $s(t)$ be the signed position relative to $O$, so that $s(0)=3\ \text{m}$.

A cart moves along a straight test track with acceleration

where $t\geq0$. At $t=0$, its velocity is $4\ \text{m s}^{-1}$ and its displacement is $-3\ \text{m}$.

Two automated carts, $A$ and $B$, move along the same straight rail. Their displacements from an origin at time $t$ seconds are

where displacement is measured in metres.

A drone moves horizontally in the positive direction. Its velocity $v\ \text{m s}^{-1}$ is related to its displacement $s\ \text{m}$ by

At $t=0$, the drone is at $s=0$.

The horizontal position of a sensor attached to a machine is modelled by

where $x$ is measured in metres and $t$ in seconds.

An elevator moves vertically, with upward taken as positive. Its velocity is

where velocity is measured in $\text{m s}^{-1}$. At $t=0$, the elevator is $4$ metres above a reference level.

A particle has acceleration

Initially, its velocity is $-\dfrac{9}{\pi}\ \text{m s}^{-1}$ and its displacement is $10$ metres.

Two runners, $A$ and $B$, move in the positive direction along a straight path. At $t=0$, runner $A$ is at the origin and runner $B$ is $9$ metres ahead. Runner $A$ has velocity $v_A=2t\ \text{m s}^{-1}$, while runner $B$ runs at a constant velocity of $6\ \text{m s}^{-1}$.

A camera drone moves along a straight tunnel. Its displacement from the tunnel entrance is modelled by

where $s$ is measured in metres, $t$ is measured in seconds and $0\leq t\leq12$.

The velocity of a ferry moving towards and away from a terminal is modelled by

where $v$ is measured in $\text{m s}^{-1}$ and $0\leq t\leq12$. Positive velocity represents motion towards the terminal.

The velocity of an experimental racing vehicle is modelled by

where $v$ is measured in $\text{m s}^{-1}$.

A ball is projected vertically upwards from a platform. Taking upwards as positive, its acceleration is modelled by

Initially, the ball has velocity $18\ \text{m s}^{-1}$ and displacement $s=0$.

The velocity of a solar-powered cart was recorded during a test. A quadratic regression model is to be used for the data.

A particle moves along a straight line with velocity

for $0\leq t\leq5$. Initially, its displacement from an origin is $2$ metres.

A particle starts at an origin and moves along a straight line. Its velocity is modelled by

where $A>0$. The particle first comes to rest at $t=\ln4$.
Here, $t$ is the numerical time in seconds, $v(t)$ and $A$ are measured in $\text{m s}^{-1}$, and displacement is measured in metres.

The velocity of a maintenance vehicle is modelled by

where $v$ is measured in $\text{m s}^{-1}$. The vehicle starts at displacement $s=-1\ \text{m}$.

A particle moves along a straight line with velocity

where $t$ is measured in seconds and $v(t)$ is measured in metres per second.

A boat moves along a straight channel. Its acceleration is

where acceleration is measured in $\text{m s}^{-2}$. Initially, the boat's velocity is $-1\ \text{m s}^{-1}$.

The position of a robotic arm along a straight guide is modelled by

where $t$ is measured in seconds, angles are in radians, and $x$ is measured in metres.

A capsule moves in the positive direction along a straight tunnel. Its speed $v\ \text{m s}^{-1}$ and displacement $s\ \text{m}$ satisfy

Initially, $s=0$.

A test vehicle moves in the positive direction along a straight track. Its acceleration depends on its displacement $s$ according to

At $s=0$, the vehicle has speed $2\ \text{m s}^{-1}$.

During a braking test, the acceleration $a$ of a car is related to its velocity $v$ by

At $t=0$, the car passes a marker with velocity $20\ \text{m s}^{-1}$ and displacement $s=0$.

A capsule moves along a straight evacuation tube. Its velocity depends on its displacement according to

where $s$ is measured in metres and $v$ in $\text{m s}^{-1}$.

An elevator undergoes a six-second acceleration phase. Its acceleration is modelled by

The elevator starts from rest and has velocity $12\ \text{m s}^{-1}$ at $t=6$.

A magnetic transport pod moves in the positive direction. Its acceleration depends on its displacement according to

At $s=0$, its speed is $1\ \text{m s}^{-1}$.

A maintenance shuttle moves along a straight rail. Its acceleration during an eight-second control cycle is

Initially, its velocity is $-2\ \text{m s}^{-1}$ and its displacement is zero.

A robotic cart has velocity

where $t\geq0$ is the numerical time in seconds, $v(t)$ is measured in $\text{m s}^{-1}$, and $k$ is a positive numerical constant.

A delivery pod travels along a straight underground route. Its velocity is modelled by

where $v$ is measured in $\text{m s}^{-1}$.

A vehicle moves along a straight road in the positive direction. During braking, its acceleration depends on its displacement $s$ from the point where braking begins according to

At $s=0$, the vehicle's speed is $12\ \text{m s}^{-1}$.