Scalars and vectors

A projectile is launched at an angle to the ground. At a particular moment, the projectile's horizontal velocity is $23.0\,\text{m s}^{-1}$ and its vertical velocity is $-10.1\,\text{m s}^{-1}$. What is the projectile's speed at this moment?

Feb/March 2017

Two positive charges and one negative charge, each with the same magnitude, are placed at the vertices of an equilateral triangle. Which diagram gives the best representation of the electric field around the charges?

Feb/March 2017

An aircraft has a speed of $200\,\text{km h}^{-1}$ in still air. The wind is blowing from the west at $85.0\,\text{km h}^{-1}$. To travel due north, in what direction should the pilot point the aircraft?

Feb/March 2019

Which pair of quantities includes one scalar and one vector?

Feb/March 2020

An equilateral triangle has charges placed at its corners: two are positive and one is negative, and all three have the same magnitude. Which diagram shows the electric field around these charges?

Feb/March 2020

A velocity vector is displayed. Its magnitude is $75\,\text{m s}^{-1}$ and it makes an angle of $30^\circ$ east of north. What are the components of the velocity vector in the northerly and in the easterly directions?

Feb/March 2021

Which diagram shows the field lines for the electric field generated by a pair consisting of one point positive charge and one point negative charge?

Feb/March 2021

Which of the following statements about scalar and vector quantities is correct?

Feb/March 2022

A projectile is fired at an angle of $25^{\circ}$ above the horizontal with a horizontal velocity component of $13\text{ m s}^{-1}$. What is the vertical component of the projectile’s velocity at the moment it is launched?

Feb/March 2024

Which quantity counts as a scalar quantity?

Feb/March 2025

A vector quantity $V$ is broken down into two perpendicular components $X$ and $Y$. The angle between $V$ and component $X$ is $\theta$. The angle between component $X$ and the vector $V$ is then increased from $0^{\circ}$ to $90^{\circ}$. In this situation, how do the magnitudes of $X$ and $Y$ vary as the angle $\theta$ is increased?

May/June 2010

A vector quantity $V$ is split into two perpendicular components $X$ and $Y$. The angle between $V$ and component $X$ is $\theta$. The angle between component $X$ and the vector $V$ is increased from $0^\circ$ to $90^\circ$. As $\theta$ is increased in this manner, what happens to the magnitudes of $X$ and $Y$?

May/June 2010

A vector quantity $V$ is split into two perpendicular components $X$ and $Y$. The angle between $V$ and component $X$ is $\theta$. The angle between component $X$ and the vector $V$ is then increased from $0^{\circ}$ to $90^{\circ}$. How do the magnitudes of $X$ and $Y$ vary as the angle $\theta$ is increased in this way?

May/June 2010

A force of $5.0\,\text{N}$ acts on a ball towards due north, and a second force of $3.0\,\text{N}$ acts on it towards due east. What is the magnitude of the resultant force on the ball?

May/June 2011

A force of $5.0\,\text{N}$ acts on a ball in the due north direction, while a second force of $3.0\,\text{N}$ acts on it due east. What is the magnitude of the resultant force on the ball?

May/June 2011

Distinguish, in terms of their properties, between scalar quantities and vector quantities.

May/June 2011

If a force $F$ shifts the point where it acts by a displacement $s$ along the direction of the force, the work $W$ done by the force is given by $W = Fs$. How many vector quantities and scalar quantities are present in this equation?

May/June 2012

A dipole consists of one positive charge and one negative charge with equal magnitude. The electric field pattern for a dipole is illustrated below. At point X, in what direction does the force on an electron act?

May/June 2012

For which quantity is the size a sensible estimate?

May/June 2012

The diagram shows a vector with magnitude $R$ and perpendicular components $P$ and $Q$. Which row gives the correct description of the perpendicular components?

May/June 2012

If a force $F$ acts so that its point of application is displaced by $s$ in the same direction as the force, the work $W$ done by the force is given by $W = Fs$. How many vector quantities and how many scalar quantities are represented in this equation?

May/June 2012

Which pair of quantities includes one vector quantity and one scalar quantity?

May/June 2013

Which pair contains one vector quantity and one scalar quantity?

May/June 2013

The diagram depicts a displacement vector with magnitude $5.0\,\text{km}$ at an angle of $53^\circ$ to the horizontal. What is the vertical component of this displacement vector?

May/June 2013

The diagrams depict a negative electric charge placed in a uniform electric field and a mass placed in a uniform gravitational field. Which row indicates the directions of the forces acting on the charge and on the mass?

May/June 2013

A cyclist is moving directly south with velocity $u$. The wind is coming from the north-east with velocity $w$. The wind’s velocity relative to the cyclist is $v$, where $v = w - u$. Which vector diagram indicates the size and direction of velocity $v$?

May/June 2013

At the vertices of an equilateral triangle, there are two positive charges and one negative charge, each with the same magnitude. Which diagram best shows the electric field around the charges?

May/June 2014

What is the vertical part of this displacement vector?

May/June 2014

Explain what a scalar quantity is and what is meant by a vector quantity.

May/June 2014

Which pair includes one vector and one scalar quantity?

May/June 2015

A positive charge and a negative charge, each with the same magnitude, are separated by a small distance. Which diagram most accurately shows the electric field associated with them?

May/June 2015

The arrow shows the vector $\vec{R}$. Which diagram does not show $\vec{R}$ split into two perpendicular components?

May/June 2015

An aeroplane travels at $200\,\text{km h}^{-1}$ in still air. The wind is blowing from the west at a speed of $85.0\,\text{km h}^{-1}$. What direction should the pilot steer the aeroplane so that it flies due north?

May/June 2015

The Sun-Earth separation is $1.5 \times 10^{11}\,\text{m}$. State this distance in $\text{Gm}$.

May/June 2015

As illustrated, three wires each apply a horizontal force to a vertical pole. Which vector diagram represents the resultant force $R$ on the pole?

May/June 2016

Which diagram could show the electric field lines between two conducting surfaces with opposite charges?

May/June 2016

The diagram illustrates two vectors $X$ and $Y$, drawn to scale. If $X = Y - Z$, which diagram most accurately shows vector $Z$?

May/June 2016

Vectors $P$ and $Q$ have been drawn to scale. Which diagram shows the vector $(P - Q)$?

May/June 2016

A ball moves from point X to point Y along a semi-circular track of radius $1.0\,\text{m}$, as illustrated. What is the ball's displacement from X to Y?

May/June 2016

Complete Fig. 1.1 to show whether each quantity is a scalar or a vector. One line has already been done as an example.

May/June 2016

A particle moves along a straight line with speed $v$. The particle decelerates and then changes direction. Its new speed is $\frac{v}{2}$. The new velocity has a component of $\frac{v}{4}$ in the same direction as the particle's original path. Through what angle has the particle turned?

May/June 2017

Which diagram most accurately shows the electric field surrounding a positive point charge?

May/June 2017

The figure presents two vectors $X$ and $Y$. These vectors are at right angles to each other. Vector $X$ has magnitude $8.0\,\text{N}$, while vector $Y$ has magnitude $6.0\,\text{N}$. What are the magnitude and direction of vector $(X - Y)$?

May/June 2017

A dipole consists of two charges with equal magnitude, one positive and the other negative. The electric field pattern for a dipole is shown. In which direction does the force act on an electron at point X?

May/June 2017

Physical quantities may be grouped as vectors or scalars. Which pair of quantities contains two vectors?

May/June 2018

As illustrated, two dogs are dragging a sledge over an icy track. Dog X exerts a pull of $200\ \text{N}$ at an angle of $65^\circ$ to the front edge of the sledge. Dog Y exerts a pull of $120\ \text{N}$ at an angle of $45^\circ$ to the front edge of the sledge. What is the resultant forward force on the sledge exerted by the two dogs?

May/June 2018

Four diagrams show the electric field between two point charges with opposite signs. Which diagram gives the correct arrangement of the electric field lines?

May/June 2018

Which pair contains a vector quantity and a scalar quantity?

May/June 2018

A force $F$ is acting at an angle $\theta$ above the horizontal. What are its horizontal component and its vertical component?

May/June 2018

State what is meant by a scalar quantity and what is meant by a vector quantity.

May/June 2018

A particle moves with velocity $V$, making an angle $\theta$ with the horizontal. Its velocity components are $V_v$ vertically upwards and $V_h$ horizontally to the right, as illustrated. What expressions give the magnitude of $V$ and the angle $\theta$?

May/June 2019

Which diagram illustrates the arrangement of the electric field lines produced by a negative point charge?

May/June 2019

Two cables are fastened to a bracket and produce forces as shown. What are the magnitudes of the horizontal and vertical components of the resultant from the two forces?

May/June 2019

As illustrated, two tugs are pulling an oil rig. The tensions in the towing cables are $4.0\,\text{kN}$ and $5.0\,\text{kN}$. What is the resultant force on the rig from the cables, measured in the eastward direction?

May/June 2019

The equation below gives the power generated when a force causes an object to move. $\text{power} = \frac{\text{work}}{\text{time}} = \frac{\text{force} \times \text{displacement}}{\text{time}}$ Which of these quantities are scalars, and which are vectors?

May/June 2020

The diagrams illustrate a negative electric charge placed in a uniform electric field and a mass placed in a uniform gravitational field. Which row indicates the directions of the forces acting on the charge and on the mass?

May/June 2020

Which of the quantities is a scalar?

May/June 2020

A dipole consists of two charges with equal magnitude: one positive and one negative. The electric field pattern for a dipole is shown below. At point X, in what direction does the force act on an electron?

May/June 2020

What features does a vector quantity have that a scalar quantity does not have?

May/June 2020

State one way in which distance and displacement are similar and one way in which they differ.

May/June 2020

A force of $10\,\text{N}$ together with a force of $5\,\text{N}$ act on an object. The angle between these two forces is $150^\circ$. The resultant force on the object may be broken down into two perpendicular components. Which row gives numerical expressions for one possible pair of perpendicular components?

May/June 2021

A body is subject to two forces: $10\ \text{N}$ vertically and $6\ \text{N}$ at $40^\circ$ to the vertical, as illustrated. What is the resultant force on the body?

May/June 2021

What is the horizontal part of the force shown?

May/June 2021

A feature that a vector quantity has, but a scalar quantity does not, is direction. For instance, velocity has direction, whereas speed does not.

May/June 2021

Two cables are fixed to a bracket and apply forces as illustrated. What are the magnitudes of the resultant’s horizontal and vertical components from the two forces?

May/June 2022

An object is travelling with an initial velocity of $4.0\ \text{m s}^{-1}$ towards the right. Its velocity then changes to a final velocity of $3.0\ \text{m s}^{-1}$ downwards, as illustrated. Which arrow shows the change in velocity of the object?

May/June 2022

Which statement is incorrect?

May/June 2022

At point P, two forces, each of $10\ \text{N}$, act as shown. The angle between their directions is $120^{\circ}$. What is the magnitude of the resultant force?

May/June 2023

One object travels straight from P to R. Another object goes from P to Q to R and takes less time. Which statement about the two objects is correct for the trip from P to R?

May/June 2023

An aircraft moves in a straight line along a level course. Two horizontal forces acting on the aircraft are the thrust force from the engines and the force produced by the wind. The vector diagram for these forces is shown. Which vector shows the resultant horizontal force on the aircraft caused by these two forces?

May/June 2023

A ball moves from point X to point Y along a semicircular track with radius $1.0\,\text{m}$, as shown. What is the displacement of the ball from X to Y?

May/June 2023

The scale drawing shows vectors $X$ and $Y$. If $X = Y - Z$, which diagram shows the vector $Z$?

May/June 2023

An object’s velocity changes from an initial velocity $u$ to a final velocity $v$. These velocities are shown by the vectors. Which one vector shows the change in velocity of the object?

May/June 2024

Which operation results in a vector quantity?

May/June 2024

What does the term scalar quantity mean?

May/June 2024

A ball hits a wall. Before the impact, the ball is moving with velocity $8\ \text{m s}^{-1}$ to the right. After the impact, it is moving with velocity $3\ \text{m s}^{-1}$ to the left. Determine the change in velocity of the ball in the collision?

May/June 2024

When two physical quantities are multiplied together, the result may be either a scalar quantity or a vector quantity. Which combination of two quantities gives a scalar quantity?

May/June 2024

Which quantity has vector properties?

May/June 2025

The two vectors, $\vec{X}$ and $\vec{Y}$, are illustrated. In which directions do $\vec{X} + \vec{Y}$ and $\vec{X} - \vec{Y}$ point?

May/June 2025

What is meant by a vector quantity?

May/June 2025

What is the component of this displacement vector in the direction $XY$?

Oct/Nov 2010

Distinguish how vector quantities differ from scalar quantities.

Oct/Nov 2010

Which set of quantities consists only of vectors?

Oct/Nov 2011

An object has two possible displacement vectors, $\vec{P}$ and $\vec{Q}$. Which vector most accurately shows the resultant displacement $(\vec{P} - \vec{Q})$ of the object?

Oct/Nov 2011

The quantities listed below may be either positive or negative. $s$ : the displacement of a particle measured along a straight line $\theta$ : the temperature reading on the Celsius scale $q$ : electric charge $V$ : the values shown on a digital voltmeter Identify which of these quantities are vectors.

Oct/Nov 2011

The diagram illustrates a non-uniform electric field around a positively charged sphere and a negatively charged sphere. Four electrons, A, B, C and D, are located at different places in the field. For which electron is the direction of the force on the electron drawn correctly?

Oct/Nov 2011

Which set of quantities consists solely of vectors?

Oct/Nov 2011

Distinguish between scalars and vectors.

Oct/Nov 2011

P and Q are vectors drawn to scale. Which diagram shows the vector $(P - Q)$?

Oct/Nov 2012

Which list includes only scalar quantities?

Oct/Nov 2012

Vectors $\vec{P}$ and $\vec{Q}$ have been drawn to scale. Which diagram shows the vector $(\vec{P} + \vec{Q})$?

Oct/Nov 2012

Physical quantities may be grouped into vectors or scalars. Which pair of quantities is made up of two vectors?

Oct/Nov 2012

Two physical quantities $P$ and $Q$ are combined. Their total is $R$, as shown. Which quantity could $P$ and $Q$ represent?

Oct/Nov 2012

The separation of two atoms in a crystal is $3.8 \times 10^{-10}\,\text{m}$. State this separation in $\text{pm}$.

Oct/Nov 2012

One object travels straight from $P$ to $R$. Another object takes a shorter time but goes from $P$ to $Q$ and then on to $R$. Which statement is correct for the two objects during the trip from $P$ to $R$?

Oct/Nov 2013

One object travels straight from P to R. A second object goes from P to Q to R in less time. Which statement is correct for the two objects on the trip from P to R?

Oct/Nov 2013

Two coplanar vectors show two forces of the same magnitude. One points east and the other points north. In what direction must a single force act so that these two forces are balanced?

Oct/Nov 2013

Which list includes one vector quantity and two scalar quantities?

Oct/Nov 2014

Which equation involves only scalar quantities?

Oct/Nov 2015

If a force $F$ shifts its point of application by a displacement $s$ in the same direction as the force, the work $W$ done by the force is $W = Fs$. How many vector quantities, and how many scalar quantities, are present in this equation?

Oct/Nov 2015