Physics · Class 11 Science
Ch 3Motion in a Plane — Class 11 Physics, concept-first.
Motion is simply a change in the position of an object with time. We see it everywhere — a toy car pushed along the floor, a cricket ball sent for a six, an aeroplane flying from one city to another — and these three everyday examples actually illustrate the three broad categories physicists use to classify motion.
Key concepts
Hover a concept to preview it and jump to its most relevant Q&A.
Projectile Motion
Imagine you throw a ball to a friend. It doesn't travel in a straight line — it rises, slows down, then curves downward and falls. That curved path is a projectile's trajectory.
Most relevant Q&A
- An object thrown from a moving bus is an example of (A) Uniform circular motion (B) Rectilinear motion (C) Projectile motion (D) Motion in o…Free
- Derive the formula for the range and maximum height achieved by a projectile thrown from the origin with initial velocity $\vec{u}$ at an an…Preview
- Show that the path of a projectile is a parabola.Preview
- A man throws a ball to a maximum horizontal distance of 80 metres. Calculate the maximum height reached.Preview
- A particle is projected with speed $v_0$ at angle θ to the horizontal on an inclined surface making an angle φ ($\phi < \theta$) to the hori…Preview
In previous exams
How often this chapter’s concepts have been examined — real appearance data, never estimated.
Chapter contents
The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.
Introduction
Motion is simply a change in the position of an object with time. We see it everywhere — a toy car pushed along the floor, a cricket ball sent for a six, an aeroplane flying from one city to another —…
Rectilinear Motion
This section builds up rectilinear (straight-line) motion quantity by quantity, using vectors, and ends with the equations of motion for uniform acceleration, free fall, and one-dimensional relative v…
Motion in Two Dimensions - Motion in a Plane
Up to this point, motion was confined to one straight line. Now the object's path is allowed to curve within a flat plane — the direction of the force on it need not coincide with the direction of its…
Average and Instantaneous Velocities
To describe an object's position in a plane, a single coordinate is no longer enough — both an x-coordinate and a y-coordinate (or, equivalently, one position vector ) are needed.
Average and Instantaneous Acceleration
The definitions of acceleration in two dimensions mirror those of rectilinear motion exactly, with each quantity now carrying x and y components.
Equations of Motion for an Object Travelling in a Plane with Uniform Acceleration
Section 3.2 derived the equations of motion for a rectilinear object moving with uniform acceleration; this section derives the corresponding equations for a particle moving in a plane with a constant…
Relative Velocity
Relative velocity between two objects moving in a plane is defined exactly as it was for rectilinear motion, but now as a genuine vector subtraction.
Projectile Motion
Any object in flight after being launched with some initial velocity, moving thereafter only under the influence of Earth's gravity, is called a projectile, and its motion is projectile motion.
Uniform Circular Motion
An object moving with constant speed along a circular path is said to be performing uniform circular motion (UCM).
Period, Radius Vector and Angular Speed
Consider an object of mass moving with uniform speed around a circle of radius . The period is the time taken to complete one full revolution — equivalently, the time to travel a distance equal to the…
Expression for Centripetal Acceleration
To find the acceleration responsible for uniform circular motion, set up coordinates with the centre of the circular path at the origin O, and let the particle start (for convenience) at point on the…
More questions
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- Q1An object thrown from a moving bus is an example of (A) Uniform circular motion (B) Rectilinear motion (C) Projectile motion (D) Motion in o…Free
- Q2For a particle having a uniform circular motion, which of the following is constant? (A) Speed (B) Acceleration (C) Velocity (D) Displacemen…Free
- Q3The bob of a conical pendulum undergoes (A) Rectilinear motion in horizontal plane (B) Uniform motion in a horizontal circle (C) Uniform mot…Preview
- Q4For uniform acceleration in rectilinear motion, which of the following is not correct? (A) Velocity-time graph is linear (B) Acceleration is…Preview
- Q5If three particles A, B and C are having velocities $\vec{v}_A$, $\vec{v}_B$ and $\vec{v}_C$, which of the following formula gives the relat…Preview
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- Q6Separate the following into groups of scalars and vectors: velocity, speed, displacement, work done, force, power, energy, acceleration, ele…Free
- Q7Define average velocity and instantaneous velocity. When are they the same?Free
- Q8Define free fall.Free
- Q9If the motion of an object is described by x = f(t), write the formulae for instantaneous velocity and acceleration.Preview
- Q10Derive equations of motion for a particle moving in a plane and show that the motion can be resolved into two independent motions in mutuall…Preview
- Q11Derive the equations of motion graphically for a particle having uniform acceleration, moving along a straight line.Preview
- Q12Derive the formula for the range and maximum height achieved by a projectile thrown from the origin with initial velocity $\vec{u}$ at an an…Preview
- Q13Show that the path of a projectile is a parabola.Preview
- Q14What is a conical pendulum? Show that its time period is given by $2\pi\sqrt{\dfrac{l\cos\theta}{g}}$, where l is the length of the string,…Preview
- Q15Define angular velocity. Show that the centripetal force on a particle undergoing uniform circular motion is $-m\omega^2\vec{r}$.Preview
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- Q16An aeroplane has a run of 500 m to take off from the runway. It starts from rest and moves with constant acceleration to cover the runway in…Free
- Q17A car moving along a straight road with a speed of 120 km/hr is brought to rest by applying brakes. The car covers a distance of 100 m befor…Free
- Q18A car travels at a speed of 50 km/hr for 30 minutes, at 30 km/hr for the next 15 minutes and then at 70 km/hr for the next 45 minutes. What…Free
- Q19A velocity-time graph is shown in the adjoining figure. [Figure: a v (m/s) versus time (s) graph with labelled points O, A, B, C, D, E; the…Preview
- Q20A man throws a ball to a maximum horizontal distance of 80 metres. Calculate the maximum height reached.Preview
- Q21A particle is projected with speed $v_0$ at angle θ to the horizontal on an inclined surface making an angle φ ($\phi < \theta$) to the hori…Preview
- Q22A metro train runs from station A to B to C. It takes 4 minutes in travelling from station A to station B. The train halts at station B for…Preview
- Q23A train is moving eastward at 10 m/sec. A waiter is walking eastward (relative to the train) at 1.2 m/sec, and a fly is flying toward the no…Preview
- Q24A car moves in a circle at the constant speed of 50 m/s and completes one revolution in 40 s. Determine the magnitude of acceleration of the…Preview
- Q25A particle moves in a circle with constant speed of 15 m/s. The radius of the circle is 2 m. Determine the centripetal acceleration of the p…Preview
- Q26A projectile is thrown at an angle of 30° to the horizontal. What should be the range of the initial velocity (u) so that its range will be…Preview