Ch 2Kinematics — Class 11 Physics, concept-first.

Physics is, at its core, an experimental science, and it rests on two pillars: experiment and mathematics.

Rest and motion are relative, not absolute. A passenger sitting in a moving bus is at rest with respect to the seat beside them, yet in motion with respect to someone standing on the pavement watching…

So far we have only spoken of where an object is. To describe motion fully we need to talk about quantities that have both a size and, often, a direction — and that calls for a sharper vocabulary than…

The magnitude (also called the norm) of a vector is the length of the arrow representing it — always a non-negative real number, regardless of which way the vector points.

Vectors are sorted into several useful families based on how their magnitudes and directions compare:

Because vectors carry direction, cannot be found by ordinary addition of the numbers and — it needs a genuinely geometric (or, equivalently, component-wise) rule.

Vector subtraction is not a new operation — it is addition of a reversed vector. To find , first construct (same magnitude as , opposite direction), then apply the ordinary triangle law of addition to…

Choosing a coordinate system lets any vector be split into perpendicular pieces along the axes — its components — turning vector problems into ordinary (scalar) algebra performed three times over, onc…

With vectors written as and , adding (or subtracting) the two vectors is the same as adding (or subtracting) their matching components: This component method is completely equivalent to the geometric…

Multiplying a vector by an ordinary number (a scalar) produces another vector, , whose magnitude is times the magnitude of .

The scalar product (or dot product) of two vectors combines them to produce an ordinary number (a scalar), not another vector — hence the name. For vectors and with angle between them,

The vector product (or cross product) of two vectors combines them to produce a third vector, not a number — hence the name.

If two vectors are equal, , then writing both in component form, forces their individual components to be separately equal: , , .

The position vector of a particle is the vector that fixes its location at a given instant, measured with respect to a chosen frame of reference/origin.

Distance is the actual length of the path travelled by an object between two instants of time — it is a scalar, and because it only ever accumulates as an object moves, distance travelled is never neg…

Writing positions as position vectors turns 'displacement' into a single vector subtraction. If a particle moves from point , with position vector , to point , with position vector , then the displace…

Any physical quantity that changes with another (usually time) is represented mathematically by a function.

Integration is, at its heart, an area-finding process, and is the reverse operation of differentiation.

The definitions of average and instantaneous velocity, speed and momentum set up in §2.9 hold for motion in any number of dimensions, in full vector form.

For a particle confined to move along the -direction, average velocity is just the change in the -coordinate divided by the elapsed time: Average velocity remains a vector quantity even in one dimensi…

When two objects A and B move with their own velocities, what an observer riding along with B actually perceives is not A's velocity by itself, but the relative velocity of A with respect to B — the r…

Consider one-dimensional motion with constant acceleration . Let be the velocity at time and the velocity at a later time .

A projectile is any object thrown into the air with some initial velocity (not purely vertical) and then left to move solely under the influence of gravity. Its path is called the trajectory.

The two flavours of projectile motion studied in this unit -- horizontal projection and angular (oblique) projection -- are both built from exactly the same two ingredients: unchanging horizontal velo…

Consider a ball thrown horizontally with speed from the top of a tower of height . It follows a curved path down to the point where it lands (call it A).

Now let the projectile be launched with speed at an angle to the horizontal (an oblique/angular projection). Resolve the initial velocity into horizontal and vertical components:

Angles can be measured in degrees or in radians; degrees are the everyday unit for 'how big a turn', while radians tie an angle directly to the geometry of a circle and are the natural unit throughout…

For a particle moving on a circle of radius about a centre O, let its position be at A at time and at B at a later time .

Uniform circular motion. When a point object moves on a circular path at constant speed, covering equal arc lengths in equal time intervals, it is said to be in uniform circular motion.

Rest and motion only make sense relative to a chosen frame of reference; physics conventionally describes position with a right-handed Cartesian coordinate system.

Sample papers and previous-year board questions for this subject.