Quick Revision Notes

Class 11 Physics - Motion in a Straight Line

MP Board

1. Introduction to Motion

Motion (गति): An object is said to be in motion if its position changes continuously with respect to its surroundings (time).
Rectilinear Motion (सरल रेखीय गति / Motion in a Straight Line): Motion of an object along a straight line path. It is also known as one-dimensional motion.
Point Object (बिंदु वस्तु): If the size of the object is much smaller than the distance travelled by it in a given time, the object is considered as a point object.

2. Distance and Displacement

Distance (दूरी): The total length of the actual path traversed by an object between its initial and final position.
- It is a scalar quantity (अदिश राशि).
- Always positive ($\text{Distance} > 0$).
Displacement (विस्थापन): The shortest straight-line distance between the initial and final position of an object.
- It is a vector quantity (सदिश राशि).
- Can be positive, negative, or zero.
- Magnitude of displacement $\le$ Distance.

3. Speed and Velocity

Speed (चाल): The rate of change of distance with respect to time. $$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$$
- Scalar quantity. SI unit: $\text{m/s}$.
Velocity (वेग): The rate of change of displacement with respect to time. $$\text{Velocity } (v) = \frac{\text{Displacement}}{\text{Time}} = \frac{x_2 - x_1}{t_2 - t_1}$$
- Vector quantity. SI unit: $\text{m/s}$.
Average Speed (औसत चाल): $$\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}$$
Average Velocity (औसत वेग): $$\text{Average Velocity} = \frac{\text{Total Displacement}}{\text{Total Time}} = \frac{x_2 - x_1}{t_2 - t_1}$$
Instantaneous Speed / Velocity (ताक्षणिक चाल / वेग): The speed or velocity of an object at a particular instant of time. $$v = \frac{dx}{dt}$$ (Derivative of position with respect to time).

4. Acceleration

Acceleration (त्वरण): The rate of change of velocity with respect to time. $$\text{Acceleration } (a) = \frac{\text{Change in Velocity}}{\text{Time taken}} = \frac{v - u}{t}$$
- Vector quantity. SI unit: $\text{m/s}^2$. Dimensional formula: $[M^0 L^1 T^{-2}]$.
Retardation / Deceleration (मंदन): Negative acceleration (when velocity decreases with time).
Instantaneous Acceleration (ताक्षणिक त्वरण): $$a = \frac{dv}{dt} = \frac{d^2x}{dt^2}$$

5. Equations of Motion (For Uniform Acceleration)

If an object moves with an initial velocity $u$, uniform acceleration $a$, and attains a final velocity $v$ in time $t$, covering a distance $s$, the kinematic equations are:

First Equation of Motion: $$v = u + at$$
Second Equation of Motion: $$s = ut + \frac{1}{2}at^2$$
Third Equation of Motion: $$v^2 = u^2 + 2as$$
Distance travelled in the $n^{\text{th}}$ second ($S_n$): $$S_n = u + \frac{a}{2}(2n - 1)$$

6. Motion Under Gravity (Free Fall)

When an object moves vertically under the gravitational pull of the Earth (neglecting air resistance):

Acceleration $a = -g$ (taking upward direction as positive, where $g \approx 9.8 \text{ m/s}^2$).
Modified Equations of Motion:
1. $v = u - gt$
2. $h = ut - \frac{1}{2}gt^2$
3. $v^2 = u^2 - 2gh$
Maximum Height ($H$): When a body is thrown upwards, final velocity $v = 0$ at the highest point. $$H = \frac{u^2}{2g}$$
Time of Ascent ($t_a$) = Time of Descent ($t_d$): $$t = \frac{u}{g}$$
Total Time of Flight ($T$): $$T = \frac{2u}{g}$$

7. Graphical Representation of Motion

Position-Time Graph ($x-t$ graph):
- Slope of $x-t$ graph = Velocity.
Velocity-Time Graph ($v-t$ graph):
- Slope of $v-t$ graph = Acceleration.
- Area under $v-t$ graph = Displacement.
Acceleration-Time Graph ($a-t$ graph):
- Area under $a-t$ graph = Change in Velocity.

8. Relative Velocity (सापेक्ष वेग)

The relative velocity of an object $A$ with respect to an object $B$ when both are moving in a straight line is given by: $$v_{AB} = v_A - v_B$$
Similarly, the relative velocity of $B$ with respect to $A$ is: $$v_{BA} = v_B - v_A$$
If objects are moving in opposite directions: $$v_{AB} = v_A - (-v_B) = v_A + v_B$$

Motion in a Straight Line

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