The magnitude of the velocity (a scalar).

Formula for position at time t with constant velocity \mathbf{v} from \mathbf{r}0?

\mathbf{r}=\mathbf{r}0+\mathbf{v}t

What is the formula for constant acceleration in terms of \mathbf{u} and \mathbf{v}?

\mathbf{a}=\dfrac{\mathbf{v}-\mathbf{u}}{t}

Final velocity from \mathbf{u}, \mathbf{a} and t?

\mathbf{v}=\mathbf{u}+\mathbf{a}t

What is a position vector?

The displacement of a point from a fixed origin.

When is an object due north of a point?

When the i (east) coordinates are equal.

When is a particle moving due north?

When the i component of its velocity is zero.

What order for change in velocity?

Final velocity minus initial velocity.

Displacement, velocity, acceleration and force as vectorsEdexcel International A Level Maths: Flashcards

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Name four vector quantities in mechanics.

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Name four vector quantities in mechanics.: Displacement, velocity, acceleration and force.
What is speed?: The magnitude of the velocity (a scalar).
Formula for position at time $t$ with constant velocity $\mathbf{v}$ from $\mathbf{r}_0$ ?: $\mathbf{r}=\mathbf{r}_0+\mathbf{v}t$
What is displacement for constant velocity?: $\mathbf{v}t$
What is the formula for constant acceleration in terms of $\mathbf{u}$ and $\mathbf{v}$ ?: $\mathbf{a}=\dfrac{\mathbf{v}-\mathbf{u}}{t}$
Final velocity from $\mathbf{u}$ , $\mathbf{a}$ and $t$ ?: $\mathbf{v}=\mathbf{u}+\mathbf{a}t$
What is a position vector?: The displacement of a point from a fixed origin.
How do you find the distance between two points with position vectors?: $|\mathbf{r}_B-\mathbf{r}_A|$
When is an object due north of a point?: When the i (east) coordinates are equal.
When is a particle moving due north?: When the i component of its velocity is zero.
Speed of $(6\mathbf{i}-8\mathbf{j})$ m s⁻¹?: 10 m s⁻¹
What order for change in velocity?: Final velocity minus initial velocity.

Exam questions on Displacement, velocity, acceleration and force as vectors

A particle moves in a horizontal plane with constant velocity $(3\mathbf{i}-4\mathbf{j})$ m s $^{-1}$ , where $\mathbf{i}$ and $\mathbf{j}$ are perpendicular unit vectors in the directions east and north. At time $t=0$ its position vector relative to a fixed origin $O$ is $(2\mathbf{i}+5\mathbf{j})$ m.
Find the position vector of the particle at $t=6$ s.2 marks
A particle moves in a plane with constant acceleration. At time $t=0$ its velocity is $(2\mathbf{i}+\mathbf{j})$ m s $^{-1}$ and 4 s later its velocity is $(14\mathbf{i}-8\mathbf{j})$ m s $^{-1}$ , where $\mathbf{i}$ and $\mathbf{j}$ are perpendicular unit vectors.
Find the magnitude of the acceleration.2 marks
Relative to a fixed origin $O$ , a ship $S$ moves with constant velocity $(4\mathbf{i}+3\mathbf{j})$ km h $^{-1}$ , where $\mathbf{i}$ and $\mathbf{j}$ are unit vectors due east and due north. At time $t=0$ (hours) the ship is at the point with position vector $(-8\mathbf{i}-5\mathbf{j})$ km. A lighthouse $L$ is at the point with position vector $(12\mathbf{i}+4\mathbf{j})$ km.
Find the position vector of $S$ at time $t$ hours. Hence find the distance of $S$ from $O$ when $t=2$ .3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).