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Acceleration = \(\frac{\DeltaV}{\Deltat}\) = \(\frac{V - U}{t_2 - t_1}\) = \(\frac{35 - 15}{20 - 10}\) = \(\frac{20}{10}\) = 2ms\(^-2\)

From S = ut + 1/2 at2 S = 1/2 ut2, since U = 0 Let S5 = distance in 5 seconds = 1/2 x 4 x 52 = 2 x 25 = 50m S4 = distance covered in 4 seconds = 1/2 x 4 x 42 = 2 x 16 = 32m Distance covered in the fifth second S5 - S4 = 50m - 32m = 18m

Power = \(\frac{work done}{time taken}\) where 1 min = 60s = \(\frac{mgh}{t}\) = \(\frac{750 \times 10 \times 90}{60}\) = 11250w or 11.25kw

coefficient of friction = \(\frac{F}{R}\) =\(\frac{F}{mg}\) = \(\frac{500}{80 \times 10}\) = 0.625

V.R = \(\frac{1}{sin\theta}\) = \(\frac{1}{sin 30^\circ}\) = \(\frac{1}{0.5}\) = 2

A moving body accelerates when: (i) Change in Speed: If the body increases or decreases its speed, it experiences acceleration, (ii) Change in Direction: Even if the speed remains constant, if the direction of the body changes (such as when turning), it still accelerates. This is because acceleration is defined as any change in velocity, and velocity includes both speed and direction.

Weight of glycerine displaced = weight of water dispalced Mgh glycerine = Mgh water Pvgh glycerine = Pvgh water 0.4V P glycerine = (0.5v)/v.4v P water = 1.25 (Polycerine)/p water = But density of substance = relative density x density of water = 1. 25 x 1000kgm3 = 1250kgm-3

Neutral Equilibrium: If the body neither returns to its original position nor increases its displacement further, it will simply adopt its new position. Examples of neutral equilibrium Ball moving on the ground. Motion of sphere. A roller. A pencil lying horizontally. An egg lying horizontally on a flat surface.

At maximum height, the final velocity, v = 0 thus from v = u - gt 0 = u - gt ∴ U = at = 10 x 4 = 40 mls

At an angle of 90^\circ, the projectile is launched straight up, maximizing its height. While other angles can also achieve significant heights, 90^\circ results in the highest possible elevation.

The sum of momentum before collision M\(_1\) U\(_1\) + M\(_2\)U\(_2\) 12 x 4.2 + 18 x 0 12 x 4.2 = 50.4 The sum of momentum after collision (m\(_1\) + m\(_2\))v = (12 + 18)v = 30v V = 50.4/30 = 1.7ms-1

Simple harmonic motion is the motion of a body whose acceleration is directed towards a fixed point and is directly proportional to its displacement from point. Statements ii, iii and v are clear examples

At vt = terminal velocity = zero acceleration = uniform velocity

When the adhesion of liquid molecules to the glass is more than the cohesion of the liquid, the liquid will wet glass.

Anomalous expansion of water is at temperature ranges 0^\circc to 4^\circc u. water contract when heated from 0^\circc to 4^\circc. thus the volume of water is least at 4^\circc