Kinematics

• Distance is the actual path travelled by an object.
• Displacement is the distance from a fixed point in a specified direction.
• Distance is a scalar quantity while displacement is a vector quantity.
• Speed is distance travelled per unit time and is a scalar quantity, while velocity is defined as the rate of change of displacement and is a vector quantity.
• Instantaneous velocity is defined as the limit of the average velocity as time interval approach zero.

  v = dr / dt
• Instantaneous speed of a particles is equal to the magnitude of its instantaneous velocity.
• Acceleration is the rate of change of velocity, and is a vector quantity.
• An object at rest would have a displacement-time graph with a zero gradient and its displacement is a constant for every second.
• An object moving at uniform velocity would have a displacement-time graph with a constant gradient and its displacement changes by a constant amount every second.
• The gradient of a displacement-time graph of an object gives the velocity of the object.
• An object at rest would have a velocity-time graph with zero gradient, meaning zero acceleration.
• An object moving with uniform acceleration would have a velocity-time graph with a constant gradient, meaning constant acceleration or deceleration.
• An object moving at uniform velocity would have a velocity-time graph with zero gradient, meaning zero acceleration.
• The gradient of a velocity-time graph of an object gives the acceleration of the object.
• An object moving with increasing acceleration would have a velocity-time graph with a positive and increasing gradient with time, meaning the velocity is increasing with time aswell.
• An object moving with decreasing acceleration would have a velocity-time graph with a positive and decreasing gradient with time, meaning the velocity is decreasing with time aswell.
• The area under the velocity-time graph gives the displacement of the object.
• An object moving with decreasing velocity would have a displacement-time graph with a decreasing gradient.
• An object moving with increasing velocity would have a displacement-time graph with an increasing gradient.
• Complete the equation:

  v = u + a*t
• Complete the equation:

  s = u*t + 1/2*a*t^2
• Complete the equation:

  v^2 = u^2 + 2*a*s
• Air resistance opposing motion tends to increase approximately with the square of the speed at high velocities and increase proportionately with speed at low velocities.
• Projectile motion deals with the motion of a body when it undergoes motion in which there is a uniform velocity in one direction and a uniform acceleration in a perpendicular direction.
• The range is the maximum horizontal distance covered by the tragectory of the projectile motion.
• Acceleration of free fall is defined as the acceleration of a body towards the surface of the Earth when the only force acting on it is its weight. It is approximately 9.81 m s^-2.