Motion

• average speed = distance travelled / time taken
• Distance-time graphs:

  • Graphs of distance against time are used to represent the motion of objects
  • Distance is plotted on the y-axis (vertical axis)
  • Time is plotted on the x-axis (horizontal axis)
  • A stationary object is represented by a horizontal straight line.
  • An object moving at a constant speed is represented by straight,sloping line
  • Speed = gradient of a distance-time graph
• Instantaneous speed --> the speed of the car over a very short interval of time. The greater the gradient, the greater the instantaneous speed
• average velocity = change in displacement / time taken
• Displacement -time graph:

  • Graphs of displacement against time are used to represent the motion of objects
  • Displacement is plotted on the y-axis
  • Time is plotted on the x-axis
  • You can determine the velocity of an object from the gradient of its displacement-time graph
• Acceleration = change in velocity / time taken
• Velocity - time graphs:

  • A straight line of constant, positive gradient : constant acceleration
  • A straight line of zero gradient : constant velocity or zero acceleration
  • A straight line of constant negative gradient : constant deceleration
  • A curve with changing gradient : acceleration is changing
  • Displacement can be found from a velocity-time graph by finding the area under the graph
• Acceleration --> the rate of change
• acceleration = final velocity - initial velocity / time taken
• displacement = (initial velocity + final velocity)/2 x time
• displacement = (initial velocity x time) + 1/2(acceleration)(time x time)
• (final velocity)^2 = (initial velocity)^2 + 2(acceleration x displacement)
• final velocity = initial velocity + (acceleration x time)
• Stopping distance --> total distance travelled from when the driver first sees a reason to stop, to when the vehicle stops
• Thinking distance --> the distance travelled between the moment when you first see a reason to stop, to the moment when you use the brake
• Braking distance --> the distance travelled from the time the brake is applied until the vehicle stops
• Thinking distance = speed x reaction time
• • Objects with a mass exert a gravitational force on each other
  • An object released on the Earth will accelerate vertically downwards towards the centre of the Earth
  • When an object is accelerating under gravity, with no other forces acting on it, it is said to be in free fall
• Determining g:

  • Electromagnet & trapdoor :- Electromagnet holds steel ball above trapdoor. When current switched off, timer triggered, the electromagnet demagnetises, and the ball falls. The value of g is calculated from the height of the fall & the time taken.
  • Light gates:- When the ball falls through the first beam, it interrupts the light & the timer starts. When the ball falls through the second beam a known distance further down, the timer stops
• Projectile motion --> form of motion experienced by an object or particle that is projected in a gravitational field
• The vertical and horizontal motions of the ball are independent of each other
• Assuming no air resistance:

  • the vertical velocity changes due to acceleration of free fall
  • the vertical displacement & time of flight can be calculated using equations of motion
  • horizontal velocity remains constant
• • the acceleration of free fall is vertically downwards
  • the component of this acceleration in the horizontal direction is zero
  • Horizontal acceleration = gcos90 = 0
• • the magnitude of the actual velocity, v, of the cannonball, or any other projectile, can be calculated from the vertical & horizontal component Vx and Vy of this velocity
• the horizontal component of the velocity is vcos theta and the initial vertical upwards components of the velocity is vsin theta
• v^2 = (vsintheta)^2 + (vcostheta)^2
• If we know the angle at which the cannonball was fired, then we can calculate its speed when it reaches maximum height.
• When the cannonball has reached its highest point, all of its kinetic energy will have been converted into potential energy
• If we know the angle at which the cannonball was fired then we can calculate its speed.
• We cannot measure the angle that the cannonball was fired at so we need another method to find out how fast it's moving.