Also known as the S.U.V.A.T. Equations S : Displacement (distance) U : Initial Velocity V : Final Velocity A : Acceleration T : Time

Learning Objectives : Starting with the motion equations from GCSE derive the 4 “S.U.V.A.T.” equations To be able to solve problems using our new “S.U.V.A.T.” equations Book Reference : Pages

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

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

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

Rewriting using our new symbols : a =v - u t Which can be rearranged as : v = u + at v = u + at

The 4 S.U.V.A.T equations (1): The first is simply our GCSE acceleration equation in the rearranged form: v = u + at v = u + at

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

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 + ½at 2

The 4 S.U.V.A.T equations (4): Combine first two equations to remove t : Multiply a = v – uand s = (u + v )t t2 as = v – ux(u + v )t t 2 t 2 Expand, simplify and rearrange : v 2 = u 2 + 2as

S.U.V.A.T Equations Summary v = u + at (1) s = (u + v)t(2) 2 s = ut + ½at 2 (3) v 2 = u 2 + 2as(4)

A worked example A driver of a vehicle travelling at a speed of 30 m/s on a motorway brakes to a standstill in a distance of 100m. Calculate the deceleration of the vehicle

A worked example Fill in (substitute) S.U.V.A.T. S = 100m U = 30m/s V = 0m/s A = ? m/s 2 T = not supplied

Choose one or more SUVAT equations which provide what we want using what we have v 2 = u 2 + 2as Rearrange a = v 2 – u 2 (0) 2 – (30) 2 2s 2(100) = -4.5 m/s 2 acceleration (4.5 m/s 2 deceleration) (4.5 m/s 2 deceleration)