Acceleration due to Gravity
What is acceleration due to gravity?
 If motion is vertical and no other forces are acting on a particle, the acceleration of the particle will be due to gravity
 Acceleration due to gravity is denoted by the letter g
 The value for gravity on Earth varies depending on location (the average value is 9.80665)
 Take g = 9.8 m s^{2} unless told otherwise
 It is often easier to leave working in terms of g as it sometimes cancels out or it can be calculated at the end
 Some questions may ask for the answer to be left in terms of g
 Gravity will always act in the downwards direction towards the earth
 If you decide upwards is the positive direction, then a = g
 If you decide downwards is the positive direction then a = g
 It is important to be clear about which direction you have decided is positive
Displacement or Distance?
 There is a difference between displacement and distance
 It is more pronounced in vertical motion problems
 Particles typically travel in both directions (up and down)
 What goes up must come down!
 Displacement, s, is a vector
 It is the position of a particle (at time t) relative to its starting position
 It only takes into account where the particle started and ended
 If a particle has returned to its starting position then its displacement will be zero
 Distance could be …
 … the distance from the start
(in which case distance is the magnitude of displacement)

 … the distance travelled
 … the distance from the origin
(the origin is not necessarily the starting position)

 … the distance from another particle
 Read the question carefully to be clear about which of these you are finding
How do I solve suvat problems involving gravity?
 Virtually the same as suvat in 1D for horizontal motion
 Follow the same steps and be careful with negatives
 You might have to spot that gravity is the acceleration by seeing the phrases:
 "falling freely"
 "projected"
 "thrown/dropped"
 A diagram is important to help make clear …
 … the positive direction of motion
 … the way in which acceleration relates to the positive direction
 … differences between displacement and distance
 Particles moving upwards will reach a maximum height
 At the maximum height, velocity is instantaneously zero, v = 0
 If you use the value 9.8 for g then your final answer must be written as a decimal to 2 significant figures
 In general the accuracy of your final answer should match the accuracy of the value used for g (1sf for g=10, 2sf for g=9.8 and 3sf for g=9.81)
Worked Example
(a) Find the maximum height the toy rocket reaches.
(b) Find the time taken from the instant the toy rocket is projected to the instant it returns to the ground.
Exam Tip
 If you are asked to find how long it takes before a particle returns to the ground, you can simply use suvat with
 s = 0 if the particle started from the ground
 s = h if the particle started a height of h m above the ground
 A common mistake is thinking that the speed of the object when it hits the ground is zero. This is incorrect! The object will be travelling with a speed at the instant it hits the ground. It is the impact that causes the speed to go to zero. For an object travelling vertically under gravity, the only time the speed is zero is when it is at its maximum height.