A stone is dropped from rest and falls for 2.5\ s. Find its speed and the distance fallen (g = 9.81\ m s^-2). [2 marks]

A projectile is launched horizontally at 15\ m s^-1. State its horizontal velocity after 2.0\ s, ignoring air resistance. [1 mark]

WJEC Eduqas Eduqas 2018-style practice: A ball is projected horizontally from the top of a cliff at 12\ m s^-1. It lands 48\ m from the base of the cliff. Calculate the height of the cliff. Take g = 9.81\ m s^-2.

Horizontal motion is at constant velocity, so the time of flight is t = horizontal distancehorizontal speed = 4812 = 4.0\ s. Vertical motion is free fall from rest: h = 12gt^2 = 12(9.81)(4.0)^2 = 12(9.81)(16) = 78\ m. Markers reward finding the time from the horizontal motion, recognising the vertical motion starts from rest with a = g, and the height about 78\ m.

WJEC Eduqas Eduqas 2020-style practice: A car accelerates uniformly from 6.0\ m s^-1 to 24\ m s^-1 over a distance of 150\ m. Calculate the acceleration and the time taken.

Acceleration from v^2 = u^2 + 2as: 24^2 = 6.0^2 + 2a(150), so 576 = 36 + 300a, giving 300a = 540 and a = 1.8\ m s^-2. Time from v = u + at: 24 = 6.0 + 1.8t, so 1.8t = 18 and t = 10\ s. Markers reward choosing v^2 = u^2 + 2as to avoid the unknown time first, the acceleration 1.8\ m s^-2, and the time 10\ s.

EnglandPhysicsSyllabus dot point

How do we describe and predict motion using graphs, the equations of constant acceleration and the idea of free fall?

Kinematics: displacement, velocity and acceleration, interpreting motion graphs by gradient and area, the equations of motion for uniform acceleration, projectiles and free fall under gravity.

A focused answer to the Eduqas A-Level Physics Component 1 kinematics content, covering displacement, velocity and acceleration, interpreting motion graphs by gradient and area, the equations of motion for uniform acceleration, projectile motion resolved into components, and free fall under gravity.

Generated by Claude Opus 4.813 min answerUpdated 2026-06-02

Reviewed by: AI editorial process; not yet individually human-reviewed

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What this dot point is asking

Eduqas wants you to define displacement, velocity and acceleration, interpret displacement-time and velocity-time graphs through their gradients and areas, apply the equations of motion for uniform acceleration, treat free fall as motion with acceleration $g$ , and analyse a projectile by separating its horizontal and vertical motion.

The answer

Displacement, velocity and acceleration

Motion graphs

The area under a velocity-time graph can be split into triangles and rectangles. The gradient of a tangent gives the instantaneous acceleration even when the motion is non-uniform.

The equations of motion

The equations apply only while the acceleration is constant. List the known quantities with a consistent sign convention (often taking the initial direction as positive), then pick the equation that fits.

Free fall

Projectile motion

A projectile launched at an angle

A ball is kicked at $20\ \text{m s}^{-1}$ at $30^\circ$ above the horizontal. Find the time of flight and the horizontal range on level ground. Take $g = 9.81\ \text{m s}^{-2}$ .

step 1: Resolve the launch velocity

Vertical: $u_y = 20\sin 30^\circ = 10\ \text{m s}^{-1}$ . Horizontal: $u_x = 20\cos 30^\circ = 17.3\ \text{m s}^{-1}$ .

step 2: Time of flight

Vertical displacement returns to zero, so use $x = u_y t - \tfrac{1}{2}gt^2 = 0$ : $t(u_y - \tfrac{1}{2}gt) = 0$ , giving $t = \dfrac{2u_y}{g} = \dfrac{2(10)}{9.81} = 2.04\ \text{s}$ .

step 3: Horizontal range

Range $= u_x t = 17.3 \times 2.04 = 35\ \text{m}$ .

Examples in context

Stopping-distance calculations combine a constant-speed thinking phase with a constant-deceleration braking phase. Sports science uses velocity-time graphs to find an athlete's acceleration phase, and projectile analysis predicts the range of a long jump or a thrown javelin. Free-fall reasoning explains why astronauts appear weightless in orbit: they and their spacecraft fall together at the same $g$ .

Try this

Q1. State what the area under a velocity-time graph represents. [1 mark]

Cue. The displacement.

Q2. A stone is dropped from rest and falls for $2.5\ \text{s}$ . Find its speed and the distance fallen ( $g = 9.81\ \text{m s}^{-2}$ ). [2 marks]

Cue. $v = gt = 24.5\ \text{m s}^{-1}$ ; $x = \frac{1}{2}gt^2 = 30.7\ \text{m}$ .

Q3. A projectile is launched horizontally at $15\ \text{m s}^{-1}$ . State its horizontal velocity after $2.0\ \text{s}$ , ignoring air resistance. [1 mark]

Cue. Still $15\ \text{m s}^{-1}$ ; the horizontal velocity does not change.

Exam-style practice questions

Practice questions written in the style of WJEC Eduqas exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

Eduqas 20184 marksA ball is projected horizontally from the top of a cliff at

12\ \text{m s}^{-1}

. It lands

48\ \text{m}

from the base of the cliff. Calculate the height of the cliff. Take

g = 9.81\ \text{m s}^{-2}

Show worked answer →

Horizontal motion is at constant velocity, so the time of flight is $t = \dfrac{\text{horizontal distance}}{\text{horizontal speed}} = \dfrac{48}{12} = 4.0\ \text{s}$ .

Vertical motion is free fall from rest: $h = \tfrac{1}{2}gt^2 = \tfrac{1}{2}(9.81)(4.0)^2 = \tfrac{1}{2}(9.81)(16) = 78\ \text{m}$ .

Markers reward finding the time from the horizontal motion, recognising the vertical motion starts from rest with $a = g$ , and the height about $78\ \text{m}$ .

Eduqas 20204 marksA car accelerates uniformly from

6.0\ \text{m s}^{-1}

24\ \text{m s}^{-1}

over a distance of

150\ \text{m}

. Calculate the acceleration and the time taken.

Show worked answer →

Acceleration from $v^2 = u^2 + 2as$ : $24^2 = 6.0^2 + 2a(150)$ , so $576 = 36 + 300a$ , giving $300a = 540$ and $a = 1.8\ \text{m s}^{-2}$ .

Time from $v = u + at$ : $24 = 6.0 + 1.8t$ , so $1.8t = 18$ and $t = 10\ \text{s}$ .

Markers reward choosing $v^2 = u^2 + 2as$ to avoid the unknown time first, the acceleration $1.8\ \text{m s}^{-2}$ , and the time $10\ \text{s}$ .

Related dot points

Sources & how we know this

Eduqas GCE AS/A Level Physics specification (A720QS) — WJEC Eduqas (2015)