1. Motion Along a Straight Line at Constant Acceleration
Also known as the S.U.V.A.T. Equations
s : Displacement (distance)
u : Initial Velocity (speed)
v : Final Velocity (speed)
a : Acceleration
t : Time

2. Learning Objectives :
Starting with the motion equations met at GCSE & derive the 4 “S.U.V.A.T.” equations (Maths jiggery pokery)
To be able to solve problems using our new “S.U.V.A.T.” equations
Book Reference : Pages

3. What can you remember from GCSE?
On your whiteboard, give a word equation for speed.
Give the correct SI units for all the quantities involved

4. From GCSE we have seen that :
Average Speed = total distance covered
total time taken
SI units :
distance (metres m)
Time (seconds s)
Making speed ms-1

5. What can you remember from GCSE?
Now rewrite this using our new “suvat” symbols :
s : Displacement (distance)
u : Initial Velocity (speed)
v : Final Velocity (speed) (use this one)
a : Acceleration
t : Time
Re-arrange so that distance is now the subject of the equation.

6. Rewriting using our new symbols :
v = s t
Which can be rearranged as :
s = vt

7. What can you remember from GCSE?
On your whiteboard, give a word equation for acceleration. Expand this as far as you can.
Give the correct SI units for all quantities involved

8. From GCSE we have seen that :
Acceleration = Change in Velocity
Time Taken for that change
Acceleration = Final Velocity – Initial Velocity
Time Taken for that change
SI units :
Initial and final velocities (ms-1)
Time (seconds s)
Making acceleration ms-2

9. What can you remember from GCSE?
Now rewrite this using our new “suvat” symbols :
s : Displacement (distance)
u : Initial Velocity (speed)
v : Final Velocity (speed)
a : Acceleration
t : Time
Re-arrange so that the final velocity is the subject of the equation.

10. Rewriting using our new symbols :
a = v - u t
Which can be rearranged as :
v = u + at
Remember that a positive value for acceleration means we are speeding up while a negative value means we are slowing down. We can also refer to negative acceleration as deceleration or retardation

11. The 4 S.U.V.A.T equations (1):
Our first equation is simply the GCSE acceleration equation in the rearranged form:
v = u + at
Write this down as “suvat” equation 1

12. The 4 S.U.V.A.T equations (2):
Looking at our rearranged speed equation:
distance = average speed x time taken
What do we mean by average?
If we start with an initial speed u, and accelerate at a constant rate to a new speed v. What is our average speed?
Hint 1 available

13. The 4 S.U.V.A.T equations (2):
Now substitute this average speed into our earlier
distance = average speed x time taken
Equation. Use the “suvat” symbols

14. The 4 S.U.V.A.T equations (2):
Starting with our rearranged speed equation: distance = average speed x time taken
Since our acceleration is uniform (constant) we know that the average (mean) speed is: = u + v 2
Substituting: s = (u + v) t 2
Write this down as “suvat” equation 2

15. The 4 S.U.V.A.T equations (3):
For equation 3, we want to eliminate v. We can achieve this by combining 1 & 2:
Substitute for v from suvat 1 into suvat 2.
Hint 2 available

16. The 4 S.U.V.A.T equations (3):
Combine first two equations to remove v :
i.e. Substitute for v from (1) into (2)
s = (u + (u + at))t 2
Rearranging: s = ut + ½at2
Write this down as “suvat” equation 3

17. The 4 S.U.V.A.T equations (4):
For equation 4, we want to eliminate t. We can achieve this by further combining 1 & 2:
Rearrange suvat 1 so that t is the subject of the equation.
Now substitute for t from our re-arranged suvat 1 into suvat 2.
Re-arrange so that v2 is the subject
Hint 3 available

18. The 4 S.U.V.A.T equations (4):
Re-arrange suvat 1 for t : t = (v –u) / a
Now substitute for t into suvat 2
s = (u + v ) (v – u)
2 a
2as = (u + v )(v – u)
2as = uv – u2 + v2 - vu
v2 = u2 + 2as
Write this down as “suvat” equation 4

19. S.U.V.A.T Equations Summary
v = u + at (1)
s = (u + v)t (2) 2
s = ut + ½at2 (3)
v2 = u2 + 2as (4)
Find these on your equation crib sheet

20. A worked example
A driver of a vehicle travelling at a speed of 30 ms-1 on a motorway brakes and comes to rest in a distance of 100m. Calculate the deceleration of the vehicle

21. A worked example
Fill in (substitute) S.U.V.A.T.
S = 100m
U = 30ms-1
V = 0ms-1
A = ? ms-2
T = not supplied

22. Choose one or more SUVAT equations which provide what we want using what we have
v2 = u2 + 2as
Rearrange
a = v2 – u2 (0)2 – (30)2
2s 2(100)
= -4.5 ms-2 acceleration
(4.5 ms-2 deceleration)