Deriving the suvat Equations (Edexcel A-Level Mathematics): Revision Notes

The SUVAT equations are used in mechanics to describe the motion of an object under constant acceleration. They relate five key variables:

• $s$: displacement
• $u$: initial velocity
• $v$: final velocity
• $a$: acceleration
• $t$: time

The equations are:

These equations apply only when acceleration is constant and are useful for solving problems involving linear motion, such as finding the distance travelled or the time taken to reach a certain velocity.

Graph**:**

• The vertical axis represents velocity v) in metres per second m/s).

• The horizontal axis represents time t) in seconds.

• The initial velocity is $u$.

• The final velocity is $v$. Gradient**:**

• The gradient of the graph represents acceleration $a$.

Rearranging**:**

Area Under the Graph:

• The area under the graph represents the displacement s). Trapezium Area Formula:

• Where s is the area between the graph and the x-axis.

Derivation**:**

• Consider the area between the line and the x-axis to be the sum of a rectangle and a triangle. Equation**:**

Substituting $v - u = at$ (from the first equation):

Derivation**:**

• Consider the area to be a rectangle with a triangle subtracted. Equation**:**

Substituting $v - u = at$:

Starting from the equation:

Square both sides:

Recognize that:

where $s = ut + \frac{1}{2}at^2$.

Thus, simplifying gives:

The SUVAT equations are provided in the formula book, but the specification outlines that you should be able to 'understand, use and derive the formulae for constant acceleration for motion in a straight line'