The velocity $v\text{ m s}^{-1}$ of a particle moving in a straight line is defined by

A particle moves in the plane. Its position vector at time $t$ seconds, $0\le t\le 4$, is

The position is measured in metres.

A particle moves in the plane with acceleration

At $t=0$, its velocity is $3\mathbf i+4\mathbf j$ and its position vector is $\mathbf j$.

A particle moves in the plane with position vector

where $t\in\mathbb R$.

A particle moves in a straight line with velocity

where $0\leq t\leq 8$, $t$ is measured in seconds and $v$ in $\text{m s}^{-1}$.

The displacement of a particle from a fixed origin is modelled by

where $0\leq t\leq 6$, $t$ is measured in seconds and $s$ in metres.

A particle moves along a straight line. Let $s$ be the numerical value of its displacement in metres and let $v$ be the numerical value of its velocity in $\text{m s}^{-1}$. They are related by

The acceleration $a$ is expressed by its numerical value in $\text{m s}^{-2}$.

The position vector of a particle at time $t$ seconds is

where $0\leq t\leq 3$ and distances are measured in metres.

A particle moves along a straight line with velocity

where $0\leq t\leq 8$, $t$ is measured in seconds and $v$ in $\text{m s}^{-1}$.

A particle moves along a straight line. Its position coordinate at time $t$ seconds is

where $0\leq t\leq 3$ and distances are measured in metres.

A particle moves in a plane with position vector

where $0\leq t\leq \pi$, $t$ is measured in seconds and distances are measured in metres. This question intentionally extends one-dimensional kinematics to planar motion; numerical integration may be used where necessary.

A particle $A$ moves in a straight line. Its displacement from a fixed origin at time $t$ seconds is given by

where $0\le t\le 6$ and $s_A$ is measured in metres.

A particle moves in a straight line with velocity

where $0\le t\le 2\pi$. Initially, the particle is $1\text{ m}$ from the origin in the positive direction.

The velocity-time graph of a particle moving in a straight line consists of straight line segments joining the points shown. The displacement of the particle from the origin at $t=0$ is $-5\text{ m}$.

A particle moves in a straight line with velocity

where $0\le t\le 5$. The particle starts at the origin. Here, $t$ is measured in seconds and $v(t)$ in metres per second.

A particle moves in three-dimensional space with position vector

where $t$ is measured in seconds and distances are measured in metres. Here $\mathbf i$, $\mathbf j$, and $\mathbf k$ are mutually perpendicular unit vectors along the positive $x$-, $y$-, and $z$-axes, respectively.

A particle moves in a straight line. Its velocity $v\text{ m s}^{-1}$ at time $t$ seconds satisfies

Initially, $v=1$ and the particle is at the origin.

A particle moves in a straight line. Its acceleration $a\text{ m s}^{-2}$ is related to its displacement $s\text{ m}$ from the origin by

When $s=0$, the particle has velocity $3\text{ m s}^{-1}$. The particle continues to move in the positive direction.

Two particles, $P$ and $Q$, move in three-dimensional space. Their position vectors at time $t$ seconds, $t\ge 0$, are

A lift moves vertically along a straight shaft. Its velocity, in $\text{m s}^{-1}$, at time $t$ seconds is modelled by

Positive velocity is upwards. At $t=0$, the lift is $2\text{ m}$ above the ground floor.

A particle moves along a straight line. Its displacement from a fixed origin at time $t$ seconds is

where $s$ is measured in metres.

The velocity-time graph of a particle moving in a straight line consists of straight line segments joining the points shown. The velocity is measured in $\text{m s}^{-1}$ and time is measured in seconds.

A projectile is launched from a point $1\ \text{m}$ above horizontal ground. Its position vector at time $t$ seconds is

where distances are measured in metres and $\mathbf j$ is vertically upwards.

A particle moves in three-dimensional space. Use the HL vector methods for three-dimensional kinematics in this question. Its position vector at time $t$ seconds is

where $0\leq t\leq 4$ and distances are measured in metres.

Two delivery carts $P$ and $Q$ move along the same straight track. At time $t$ seconds, $P$ has velocity $v_P(t)=2+3e^{-t/2}$ and starts from the origin. Cart $Q$ starts $18\ \text{m}$ ahead of $P$ and moves with constant velocity $1\ \text{m s}^{-1}$.

A particle moves along a straight line. Its acceleration at time $t$ seconds is

where $0\le t\le \pi$. Initially its velocity is $-1\text{ m s}^{-1}$ and it is at the origin.

A particle moves along a straight line with velocity

where $0\le t\le \ln 16$. The particle starts at the origin.

Two particles $P$ and $Q$ move along a straight line. Taking a fixed positive direction along the line, the signed relative displacement of $P$ from $Q$ at time $t$ is

where $t$ is the numerical value of the time in seconds and $0\le t\le 3$.

A particle moves in a straight line. Its velocity $v\text{ m s}^{-1}$ satisfies the differential equation

At $t=0$, the particle is at the origin and has velocity $5\text{ m s}^{-1}$.

Two small robots, $P$ and $Q$, move along the same straight track. At $t=0$, robot $P$ is at the origin and robot $Q$ is $18\ \text{m}$ ahead of $P$. Their velocities, in $\text{m s}^{-1}$, are

for $0\le t\le 20$.