Integrated Science

• The Law of Acceleration

  - The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force in the same direction as the net force and inversely proportional to the mass of the object. In order to get more acceleration, you need to apply higher force.
• Acceleration - rate of change in velocity with time. It is a vector quantity having both magnitude and direction.
• Acceleration - The value of the acceleration is constant. It does not change. The velocity changes but at a constant rate. an object with zero acceleration is said to be in Uniformly Accelerated Motion and has non-zero but constant acceleration
• $d=$$V_{i}t+$$\frac{at^2}{2}$

  • Kinematic Equation 1
• $V_{f}=$$at+$$V_{i}$

  • Kinematic Equation 2
• $d=$$\frac{1}{2}(V_{f}+$$V_{i})t$

  • Kinematic Equation 3
• $V_{f}^2=$$V_{i}^2+$$2ad$

  • Kinematic Equation 4
• Objects at free fall also exhibit uniformly accelerated motion
• The acceleration due to gravity on Earth's surface is approximately 9.8 m/s².
• It is a constant acceleration of all falling bodies, regardless of their mass and weight.
• In general, UAM is the one in which the acceleration of a body throughout the motion is uniform. It can be observed in either vertical or horizontal dimensions and in two dimensions.
• Projectile - an object undergoin projectile motion
• Trajectory - the curve like motion path undergone by a projectile.
• Angle - a numerical value in degrees expressing the orientation of the projectile to be thrown projected.
• Projectile motion consists of horizontal and vertical motion working independently
• Horizontal Motion (X Component)

  • Neglects air resistance
  • There is a constant horizontal velocity. Vx
  • Horizontal Acceleration is 0. ax=0
  • We call horizontal distance as range. dx
• Vertical Motion (Y Component)

  • The force acting is gravity (g = ay=ag). g=9.82 m/s^2
  • Vertical velocity is not constant. Vy
  • We call the vertical distance as the height. h=dy
• Height - the vertical distance from the projectile to the earths surface.
• Range - horizontal distance covered
• $V_{x}$

  • Horizontal velocity
• $V_y$

  • Vertical velocity
• $d_y=$$\frac{1}{2}agt^2$

  • Formula for height
• $t=$$\frac{d_x}{V_i}$

  • Formula for time
• $d_y=$$\frac{(V_i * sinx)^2}{2ag}$

  • Formula for height
• $d_x=$$V_i*$$cosx*$$t$

  • Formula for range
• $t=$$2(\frac{V_i *sinx}{ag})$

  • Formula for time
• The word momentum (plural, momenta) is Latin and means “movement” or “inertia in motion”. Operationally, momentum is defined as the product of mass and velocity. It is expressed in units like kilogram - meter/second (kg.m/s) or Newton - second (N.s).
• Momentum can be defined as "mass in motion." If an object is at rest, it has no momentum. All objects have mass. So, if an object is moving, then it has momentum. It has its mass in motion.
• The amount of momentum that an object has is dependent upon two variables:

  • how much stuff is moving
  • how fast the stuff is moving
• Whenever a force is applied on an object, the momentum of the object changes. Applying a slight force on a vehicle and it yields a small change in momentum. The time of contact is also an important factor. Applying same force for a longer time and an immense change of momentum happens. A longer sustained force produces large change in momentum or impulse. The momentum of an object also changes if its velocity and/or mass also changes