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# Kinematics

The equations of motion given in the diagram can be used to calculate displacement, initial and final velocity, acceleration and time, provided that three of these variables are known. These equations can be used only when the acceleration is uniform and when the object is travelling in a straight line. For an object falling vertically downwards, acceleration can be moddeled to be equal to g = 9.8 m/sยฒ. For an object that is dropped, the inital velocity can be assumed to be 0.

The normal force is the support force exerted onto an object by another stable object that it is in contact with. The friction force is the force which opposes the direction of motion exerted by a surface onto an object moving or trying to move across it. The maximum value of the friction force F = ฮผR, where ฮผ is the coefficient of friction and R is the normal force, is reached when the body it is acting on is in limiting equilibrium, ie. about to move.

Problems involving objects on slopes can be solved by resolving forces perpendicularly and parallelly to the slope, rather than horizontally and vertically. The angle the slope makes with the horizontal is equal to the angle the weight of the object makes with the line perpendicular to the slope.

An object thrown into the air follow a parabolic path called a trajectory; this is called a projectile. This object will move under the influence of gravity. Since gravity acts downwards, it only affects the vertical velocity of the object. Equations of motion can be used to calculate the vertical velocity. There are no horizontala forces acting on the projectile, since air resistance is usually neglected, so the horizontal velocity remains constant during the time of flight and the equation velocity = distance/time can be used. The object travels upwards at a decreasing rate, until its velocity becomes 0 and it starts to accelerate towards the ground. Gravity also affects objects that are falling vertically. At the beginning, the only force acting on the object is its own weight, so the object accelerates downwards. As the velocity of the object increases, the drag forces acting on it increases. At some point, the drag force will balance the weight force and there is no resultant force acting on the object, therefore by Newton's First Law, it will continue to fall at constant velocity; this is called terminal velocity.

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