3.4 More on velocity time graphs | 3.5 Equations of motion

How do you find displacement from a velocity time graph?

By finding the area under the graph

What does suvat stand for?

s = Displacement or distance travelled

u = initial velocity

v = final velocity

a = acceleration

t = time taken

What does the velocity time graph for an accelerating object look like?

The initial velocity of the object is u. After a time t the final velocity of the object is v. The object has constant acceleration a.

Gradient = (v - u) / t

Triangular Area = ½ × (v - u) × t

Rectangular Area = u × t

What is the equation of motion without s?

a = change in v/ change in t = (v - u)/t

This can be rearranged to give:

v = u + at

What is the equation of motion without v?

The area under a velocity time graph is equal to displacement s.

The rectangular area: ut

The triangular area: ½ × (v - u) × t

From (v - u) = at. If you substitute this into the expression for area of a triangle you get:

s = ut + ½ at²

What’s the equation of motion without a?

If you treat the area under the graph as the area of a trapezium (with u and v as the parallel sides of the trapezium, and t as the perpendicular separation between them this becomes:

s = ½ (u + v)t

What is the equation of motion without t?

Time is given by: t = (v - u) / a

Thus can be substituted into s = ½ (u + v)t to give s = ½ (u + v) × (v - u)a

Rearranging this gives:

(u + v)(v - u) = 2as

Which gives:

V² = u² + 2as