CBSE Class 10 Physics Motion Notes Set 11

Motion, Rest and Types of Motion

An object is in motion when its position changes with time relative to a chosen reference body, and at rest when it does not. Both states are relative: passengers in a moving bus are at rest with respect to one another but in motion with respect to a roadside pole.

1. Rectilinear motion: along a straight line (one dimension).
2. Rotational motion: turning about a fixed axis, such as a fan or the spinning Earth.
3. Two-dimensional motion: in a plane, such as circular or projectile motion.
4. Three-dimensional motion: in space, such as a flying bird.

Distance and Displacement

Distance is always greater than or equal to the magnitude of displacement. They are equal only for motion along a straight line without reversing. A complete round trip gives zero displacement.

Speed and Velocity

Speed = distance / time (scalar, never negative). Velocity = displacement / time (vector). In SI both are measured in m/s, and 1 km/h = 5/18 m/s.

1. Uniform speed: equal distances in equal intervals of time.
2. Average speed = total distance / total time.
3. Average velocity = total displacement / total time.
4. Average speed is always at least the magnitude of average velocity.
5. A speedometer shows instantaneous speed.

For a journey in a straight line, with distances x1, x2, ... covered at speeds v1, v2, ...: \( v_{avg} = \dfrac{x_1+x_2+\cdots}{x_1/v_1 + x_2/v_2+\cdots} \). For two equal distances: \( v_{avg} = \dfrac{2v_1v_2}{v_1+v_2} \). For two equal times: \( v_{avg} = \dfrac{v_1+v_2}{2} \).

Acceleration

Acceleration is the rate of change of velocity: \( a = \dfrac{v-u}{t} \). Its SI unit is m/s\( ^2 \) (CGS: cm/s\( ^2 \)). It is a vector. When speed decreases, acceleration points opposite to velocity and is called retardation. Motion with zero acceleration is uniform motion.

Equations of Uniformly Accelerated Motion

1. \( v = u + at \)
2. \( s = ut + \tfrac12 at^2 \)
3. \( v^2 = u^2 + 2as \)
4. Distance in the nth second: \( s_n = u + \dfrac{a}{2}(2n-1) \)

Here u is initial velocity, v final velocity, a acceleration, t time and s displacement. For a body starting from rest, distances in successive equal intervals are in the ratio 1 : 3 : 5 : 7 and total distances in 1 s, 2 s, 3 s are in the ratio 1 : 4 : 9.

Motion Under Gravity

Free fall is motion under gravity alone, with acceleration g = 9.8 m/s\( ^2 \) downward (often taken as 10). Taking upward as positive, a = -g.

1. Dropped from height h: time of fall \( t = \sqrt{2h/g} \), speed on landing \( v = \sqrt{2gh} \).
2. Thrown upward with speed u: maximum height \( H = u^2/2g \), time to top = u/g, total time of flight = 2u/g.
3. At the highest point velocity is zero but acceleration is still g.
4. Time of fall does not depend on mass.

Graphs of Motion

1. Slope of a distance-time (or displacement-time) graph gives speed (or velocity); a straight line means uniform motion.
2. A horizontal line on a velocity-time graph means constant velocity and zero acceleration.
3. Slope of a velocity-time graph gives acceleration.
4. Area under a velocity-time graph gives displacement; area under an acceleration-time graph gives change in velocity.

Worked Examples

Example 1. A car moving at 20 m/s brakes with a retardation of 5 m/s\( ^2 \). Find the stopping distance. Solution: \( s = u^2/2a = 400/10 = 40 \) m.

Example 2. A stone is dropped from a 45 m high tower. Find the time to land (g = 10 m/s\( ^2 \)). Solution: \( t = \sqrt{2 \times 45/10} = 3 \) s.

Example 3. A body goes 60 km at 30 km/h and returns 60 km at 60 km/h. Average speed = 120 / (2 + 1) = 40 km/h, and average velocity is zero.