
Explore kinematics across one dimension and two dimensions, from basic to advanced concepts, including vectors and calculus, to prepare grade 11–12 students for physics and engineering or medical entrance exams.
Kinematics is a subfield of physics, developed in classical mechanics, that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause them to move.[1][2][3] Kinematics, as a field of study, is often referred to as the "geometry of motion" and is occasionally seen as a branch of mathematics.[4][5][6] A kinematics problem begins by describing the geometry of the system and declaring the initial conditions of any known values of position, velocity and/or acceleration of points within the system. Then, using arguments from geometry, the position, velocity and acceleration of any unknown parts of the system can be determined. The study of how forces act on bodies falls within kinetics, not kinematics.
Define position as an object's location on a fixed origin line, with positive to the right and negative to the left, and distinguish distance traveled from displacement.
Position time graph and calculating average speed from position time graph
Distance-time graphs
A distance-time graph shows how far something travels over a period of time. The vertical axis of a distance-time graph is the distance travelled from the start. The horizontal axis is the time from the start.
Features of the graphs
When an object is stationary, the line on the graph is horizontal. When an object is moving at a steady speed in a straight line, the line on the graph is straight but sloped.
Calculating speed or velocity from position time graph
Average speed
When an object moves in a straight line at a steady speed, you can calculate its average speed if you know how far it travels and how long it takes. The following equation shows the relationship between average speed, distance moved and time taken:
average speed=distance moved/time taken
average speed is measured in metres per second, m/s
distance moved is measured in metres, m
time taken is measured in seconds, s
For example, a car travels 300 m in 20 s. Its average speed is:
300 ÷ 20 = 15 m/s
The velocity of a particle is a vector quantity that describes the magnitude as well as direction of motion of the particle. More mathematically, the rate of change of the position vector of a point, with respect to time is the velocity of the point. Consider the ratio formed by dividing the difference of two positions of a particle by the time interval. This ratio is called the average velocity over that time interval and is defined as
Vavg= Delta r/delta t
whereDelta r is the change in the position vector during the time interval Delta t.
In the limit that the time interva Delta t approaches zero, the average velocity approaches the instantaneous velocity, defined as the time derivative of the position vector,
The speed of an object is the magnitude of its velocity. It is a scalar quantity:
v=IvI= ds/dt
where s is the arc-length measured along the trajectory of the particle. This arc-length must always increase as the particle moves. Hence, ds/dt is non-negative, which implies that speed is also non-negative.
By analysing the the units for the slope of velocity time graph , m/s2 you can detrmine acceleration of the object. The motion of bike taken in this example is a non uniform motion . position time graph is curved concave downward indicating velocity is decreasing and acceleration is negative . velocity time graph is a straight line with negative slope suggesting negative acceleration or retarded motion .
Derive displacement and acceleration from velocity-time graphs by calculating areas under the curve and the slope of the graph, with examples using rectangular and trapezoidal regions and positive/negative velocities.
Ball thrown upward shows velocity decreasing to zero at the highest point and becoming negative on descent under constant downward gravity, illustrating uniformly accelerated motion and velocity-time and displacement-time graphs.
Illustrates how to compute average velocity as total displacement over total time and acceleration as the change in velocity over time, using eastward motion and displacement examples.
Learn how vectors represent force and motion in one and two dimensions, determining magnitude and direction. Decompose vectors into x and y components and find resultant displacement.
Explore motion in two dimensions by analyzing vectors, resolving components, and calculating displacement, including diagonal motion on a football field and navigation methods.
Apply relative motion to compute the plane's air velocity for a 250 km west path in 2.5 hours, given a 40 km/h wind at 65 degrees north of west.
Resolve the river boat problem by decomposing a 10.1 km/h velocity at 23 degrees into components, then compute ground displacement to arrive at about 77.4 seconds.
Examine projectile motion as two-dimensional motion with a parabolic path. Identify horizontal velocity remains constant while vertical velocity changes due to gravity; define range and initial velocity components.
Crack the toughest physics problems on 1D and 2D motion with this exam-focused course designed for AP Physics, JEE, NEET, and other competitive exams. Whether you're aiming for perfect scores or struggling with kinematics concepts, this course transforms confusion into clarity through structured theory, shortcut methods, and 200+ exam-style problems.
What You'll Master:
1D Motion (Straight-Line Physics)
✓ Equations of Motion with calculus/non-calculus approaches (AP-aligned)
✓ Graphs (x-t, v-t, a-t) and their problem-solving applications
✓ Relative motion tricks for river-swimmer problems (favorite in Exams!)
✓ Variable acceleration problems using integration (Advanced AP Level)
2D Motion (Projectiles & Vectors)
✓ Projectile Motion from ground/cliff with air resistance approximations
✓ Circular Kinematics: Centripetal force, angular velocity and conical pendulum problems
✓ Relative Motion in 2D (Boat-river, wind-adjusted flights - 75% repeat rate in exams
✓ Parabolic Trajectory optimization (Range/Height trade-offs - hot topic)
This course on motion in 1dimention and 2dimention have been made for students studying physics in grade 11 and 12th. In this course you will learn about scaler and vector Physical quantities, uniform motion , non uniform motion. Define qualitatively and quantitatively displacement velocity and acceleration .
Numerical based on displacement velocity , average velocity and acceleration.
Explain uniform and uniformly accelerated motion when provided with written descriptions and numerical and graphical data. Analyzing velocity time graphs .
Addition and subtraction of vectors and their application in Kinematics. Resolution of vectors and their application in Kinematics . Adding vectors using components. Adding two dimensional vectors graphically. Determining components. Adding Vectors using components. Polar coordinator method and navigator method and using them to solve problems vectorially. Adding non collinear vectors graphically and problems based on them.
Explain two dimensional motion in a horizontal or vertical plane and interpret motion of one object relative to other. Relative motion in air , non -collinear relative motion , Relative motion in water .Problems based on velocity of airplane with respect to wind and velocity of boat with respect to river.
Analyzing Projectile motion, horizontally projected projectiles and obliqully projected projectile motion. Range , maximum height and time of flight of projectiles. Numerical based on projectiles projected horizontally and obliqually.
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Instructor: [GAGAN DEEP AHUJA]
• Senior faculty Physics
• 25+ Years Training JEE/NEET Top-100 Rankers