1. A –Level Physics: Kinematics- SUVAT equations

2. Objectives: Additional skills gained: Advanced calculation
Spec point 9: be able to use the equations for uniformly accelerated motion in one dimension using SUVAT equations
Spec point 15: understand how to make use of the independence of vertical and horizontal motion of a projectile moving freely under gravity
Additional skills gained:
Advanced calculation
Component Isolation

3. Lesson-Link: The string of beads…
You have 10mins to figure it out….

4. What is Kinematics?
KINEMATICS
Scientific
Study
Motion

5. What you’ll be able to calculate

6. NO ACCELERATION OCCURRING!
From simple…
What is the simplest equation you can think of that relates distance, speed and time?
s = 𝒅 𝒕
v = 𝒔 𝒕
Convert this into a vector form
You use this equation when there is
NO ACCELERATION OCCURRING!
Careful! Displacement is shown by an ‘s’ but it’s not representing speed!

7. To complex…
So far, we have covered equations for constant motion but without acceleration. So how do we deal with motion with constant acceleration?....
SUVAT
It’s an acronym! Write the word nice and big and using colours! For each one, annotate what it represents and the unit it is measured in!

8. Unravelling the maths…
Don’t forget as we’re going through this that these equations only work with constant acceleration and that often the value for acceleration can be substituted for ‘g’ as gravitational force is commonly used in questions!
SUVAT
Task: We are soon going to start a flow chart of the equations! Start these on a new page with clear highlighting of the equations.

9. Rearrange the equation for acceleration to have v as the subject
SUVAT
Step 1, equation 1
Rearrange the equation for acceleration to have v as the subject
𝒂= 𝒗−𝒖 𝒕
𝒗=𝒖+𝒂𝒕

10. Try combining this with the equation for non-acceleration displacement
SUVAT
Step 2, equation 2 u
If acceleration is constant then what is the average velocity of a journey between two points? 𝒖 𝒗
𝒖+𝒗 𝟐
a.k.a
Average ‘v’
Try combining this with the equation for non-acceleration displacement
(s= v x t)
s = ( 𝒖+𝒗 𝟐 ) ×𝒕

11. Work out the simplest form…
SUVAT
1 + 2 makes equation 3! u
We need to combine the first and second equations. Let’s try first to do it by putting the first into the second…
𝒗=𝒖+𝒂𝒕
s = ( 𝒖+𝒗 𝟐 ) ×𝒕
Work out the simplest form…

12. Work out the simplest form…
SUVAT
1 + 2 makes equation 3!
Work out the simplest form… u
𝐬= (𝐮+ 𝐮+𝐚𝐭 ) 𝟐 ×𝐭
𝐬= 𝟐𝐮+𝐚𝐭 𝟐 ×𝐭
𝐬=𝐮𝐭+ 𝟏 𝟐 𝐚𝐭𝟐
𝐬= 𝟐𝐮𝐭+𝐚𝐭𝟐 𝟐
𝐬=𝐮𝐭+ 𝟏 𝟐 𝐚𝐭𝟐

13. 1 + 2 makes equation 4…as well…
SUVAT
1 + 2 makes equation 4…as well… u
If we combine the equations again but this time changing equation 1 to be in the form of t….
𝒗=𝒖+𝒂𝒕
s = ( 𝒖+𝒗 𝟐 ) × (𝒗−𝒖) 𝒂
2as = 𝒖+𝒗 ×(𝒗−𝒖)
s = ( 𝒖+𝒗 𝟐 ) ×𝒕
2as = 𝒖𝒗+𝒗𝟐−𝒖𝟐−𝒗𝒖
𝒕= 𝒗−𝒖 𝒂
v2 = 𝒖𝟐+𝟐𝒂𝒔

14. SUVAT What we haven’t got…
Make a table whereby you have all of the equations on the left hand side, and the quantity that is missing each time. If the SUVAT doesn’t contain the needed variable then don’t use it!

15. Worked Example We want: v We have: t
A man drops a rock from the top of a cliff and the rock takes 3 second to reach the bottom. Calculate both the velocity it reaches before hitting the ground and the distance it fell
Pick the Equation:
Which equation contains the quantity we want and a quantity we know?
Only two equations have both, and
We can’t use the first one as it contains ‘s’ which we do not know yet! So we use the second!
We want: v
We have: t
𝐬=𝐮𝐭+ 𝟏 𝟐 𝐚𝐭𝟐
𝒗=𝒖+𝒂𝒕
Rearrange:
Rearrange the equation to make the needed quantity the subject. Luckily in this case we don’t need to!
3. Plug the values in:
We know that time here is 3s, we know that the initial velocity was 0ms-1 and acceleration must be 9.81ms-2.
𝒗=𝒖+𝒂𝒕
𝒗=𝟎+(𝟗.𝟖𝟏 ×𝟑)
𝒗=𝟐𝟗.𝟒ms-1

16. Worked Example We want: s We have: t and v
A man drops a rock from the top of a cliff and the rock takes 3 second to reach the bottom. Calculate both the velocity it reaches before hitting the ground and the distance it fell
Repeat for the other quantity:
Which equation contains the quantity we want and a quantity we know?
Two equations can be used here: and
Solving for ‘s’ gives us 44.1m!
We want: s
We have: t and v
𝐬=𝐮𝐭+ 𝟏 𝟐 𝐚𝐭𝟐
v2 = 𝒖𝟐+𝟐𝒂𝒔
The key to SUVAT calculations is just to spend a little time working out the correct equation to use!

17. Practice Questions
A bird drops a stone from 88m above a pond, how long will it take the stone to hit the surface and what speed will it be travelling at just before it hits the water?
An alien is holidaying on Pluto and throws a tennis ball vertically upward at a speed of 20ms-1 causing it to reach the peak of its journey a whopping 303m above the point of release. Calculate the acceleration due to gravity on Pluto

18. Extension/IS
Write
Force for one = cos 35 x 6500 = Both = 10648N. A= F/m = 10.6ms-2

19. Objectives: Additional skills gained: Advanced calculation
Spec point 9: be able to use the equations for uniformly accelerated motion in one dimension using SUVAT equations
Spec point 15: understand how to make use of the independence of vertical and horizontal motion of a projectile moving freely under gravity
Additional skills gained:
Advanced calculation
Component Isolation