P7 on the move

• displacement is distance in a given direction
• speed is change of distance per unit time
• velocity is speed in a given direction, it is change of displacement per unit time
• speed and distance are scalar quantities
• velocity and displacement are vector quantities
• the equation for speed: v = s/t

  v = speed in ms^-1

  s = distance in m

  t = time in s
• the gradient of a distance-time graph is the speed of the object
• the gradient of a displacement-time graph is the velocity of the object
• acceleration is the change of velocity per unit time
• the unit of acceleration is ms^-2
• acceleration is a vector
• equation for acceleration: a = (v-u)/t

  a = acceleration in ms^-2

  v = final velocity in ms^-1

  u = initial velocity in ms^-1

  t = time in s
• deceleration values are negative, which shows that velocity is decreasing over time, so the object is slowing down
• uniform acceleration is when the velocity of an object, moving along a straight line, changes at a constant rate, so the acceleration is constant
• non-uniform acceleration is when the direction or speed of an object moving changes at a varying rate, so the acceleration is variable
• the gradient of a velocity-time graph is acceleration
• constant acceleration means you can use a set of equations called the SUVATs, they are:

  v = u + at

  s = 1/2(u+v)t

  s = ut + 1/2(at^2)

  v^2 = u^2 + 2as
• the area under a velocity-time graph is displacement
• when an object is in free fall, there are no forces acting on it apart from gravity
• the acceleration of free fall is represented by g, at the earth’s surface it is 9.8 ms^-2
• usually, assign the upwards direction as positive and the downwards direction as negative
• the difference between a distance-time graph and a displacement-time graph is that distance will always be increasing, but displacement can decrease
• the difference between a speed-time graph and a velocity-time graph is that the area under a speed-time graph is the distance, and the area under a velocity-time graph is the displacement
• only use the SUVAT equations if the acceleration is constant, not variable
• if a problem has multiple stages with different accelerations you can split it up and use SUVATs for each stage with constant accelerations
• a projectile is any object acted upon only by the force of gravity
• there are three key principles of projectile motion:

  • acceleration of the object is always equal to g and is always downwards, so there is no horizontal acceleration
  • horizontal velocity is constant because there is no horizontal acceleration
  • motions in the horizontal and vertical directions are independent
• if the initial velocity is at an angle, draw a triangle and use trigonometry to resolve it to get the horizontal and vertical initial velocity
• when working with constant acceleration, write out SUVAT and all the known values to work out which equation to use
• the path of a projectile is parabolic, you can use the symmetry to help with questions as the time to reach maximum height is half of the total time
• a projectile moving through air experiences a drag force due to air resistance, this acts in the opposite direction to its motion
• many questions will specify to ignore the effects of air resistance