• The kinematic equations of motion are a set of four equations which can describe any object moving with?constant?acceleration
• They are often referred to as the 'suvat' equations due to the variables they include
• These are:
  • s?=?displacement?(m)
  • u?=?initial velocity?(m s?1)
  • v?=?final velocity?(m s?1)
  • a?=?acceleration?(m s?2)
  • t?=?time interval?(s)

• The four SUVAT equations are:

• These are all given on the data sheet
• All the variables, apart from?time?t, are vector quantities
  • This means they can either be positive or negative depending on their direction

Mastering the SUVAT Equations

• The SUVAT equations are?always?used when acceleration is constant, but not zero

• This is indicated in questions by
  • An explicit statement that an object is?'constantly accelerating'?or?'constantly decelerating', or words to that effect
  • A description of an object in freefall where either?'air resistance can be ignored'?or?'air resistance is negligible'
  • A statement that an accelerating or decelerating force is constant, since?F = ma, constant force → constant acceleration

• Questions may appear to be missing some information, this should be checked before starting to calculate
  • Objects in motion often start or end at rest, making either?u?or?v?= zero
  • Objects in freefall have a?constant?acceleration of 9.81 m s?2
  • When an object is slowing down it has a?negative?value for acceleration, this must be included in the calculation
  • Objects thrown or shot upwards also have negative acceleration (since they are?slowing down?as they ascend) and reach a?final velocity of zero?at the top of their path

Step 1: List the known values

• • Length of the runway,?smax?= 450 m (this is the maximum value of displacement)
  • Initial velocity,?u?= 40 m s?1
  • Final velocity,?v?= 0 m s?1?(since the plane will stop)
  • Acceleration,?a?= ? 2 m s?2?(the negative sign indicates slowing down)

Step 2: Identify the missing values (the unknown answer and the one not given)

• • Known quantities:?u,?v?and?a
  • Unknown quantity: displacement,?s
  • Time,?t?is not required in this question

Step 3: Choose the correct SUVAT equation and rearrange it

• • The SUVAT equation which contains?u,?v,?a?and?s?and omits?t?is:

v2?=?u2?+ 2as

• • Rearrange to make?s?the subject:

Step 4: Substitute the values into the equation and calculate?s

Step 5: Write the full answer to the question

• • The plane stops after 400 m, which is 50 m before the end of the runway

• • Note:?In this solution, the negative value produced by?v2?? u2?is cancelled out by the negative value for acceleration, giving a positive value for displacement

Part (a)

Step 1: List the known values

• • Initial velocity,?u?= 0 m s?1
  • Acceleration,?a?= 6.5 m s?2?(the positive sign indicates the speed is increasing due to the motor)
  • Time,?t?= 30 s

Step 2: Identify the missing values (the unknown answer and the one not given)

• • Known quantities:?u, a,?t
  • Unknown quantity: final velocity,?v
  • Displacement,?s, is not required in this question

Step 3: Choose the correct SUVAT equation

• • The SUVAT equation which omits displacement,?s, is:

v?=?u?+?at

Step 4: Substitute the values into the equation and calculate

v?= 0 + (6.5 × 30) = 195 m s?1

Step 5: Write the full answer to the question, taking care to check significant figures

• • The final velocity,?v, at 30 s is 200 m s?1?(2 s.f.)

Part (b)

Step 1: List the known values

• • Initial velocity,?u?= 0 m s?1
  • Acceleration,?a?= 6.5 m s?2
  • Time,?t?= 30 s
  • Final velocity,?v?= 195 m s?1

Step 2: Identify the missing values (the unknown answer and the one not given)

• • Known quantities:?u, a,?t, and?v?(from part a)
  • Unknown quantity: final displacement,?s
  • All the SUVAT values are available in this case, but since?v?was calculated, first look for an equation that doesn't use it (in case of mistakes)

Step 3: Choose the correct SUVAT equation

• • The SUVAT equation which omits velocity is:

s?=?ut?+ at2

Step 4: Substitute the values into the equation and calculate?s

s?= (0 × 30) + (6.5 × 302) = 2925 m

Step 5: Write the full answer to the question, taking care to check significant figures

• • The height,?s, above the launchpad is 2900 m (2 s.f)