**Acceleration**

It is defined as the rate of change of velocity.

Average acceleration= (change in velocity)/(time taken)

a=Δv/Δt

a=(v-u)/t

Where v= final velocity and u= initial velocity.

**Equations of motion**

**Symbols**

Displacement = s

Initial velocity= u

Final velocity = v

Acceleration= a

Time= t

** **

**Equations of motion**

**Equation 1**

If we start with the equation for acceleration a=((v-u))/t we can rearrange this to give us an equation 1

at=(v-u) ~ at+u=v

Equation 2

We start with the definition of velocity and rearrange for displacement,

Velocity = displacement/time

Displacement = velocity × time

According to given graph, we need to use the average velocity,

Displacement = average velocity × time

average velocity= ((u+v))/2

We now substitute this into the above equation,

s=((u+v))/2 t

s=1/2 (u+v)t

Equation 3

With equation 1 and 2 we can derive equation which eliminate v. by substituting,

v=u+at Into s=1/2 (u+v)t

s=1/2 (u+( u+at))t

s=ut+ 1/2at^2

Equation 4

If we rearrange equation 1 into t=((v-u))/a which will then substitute into equation2:

v^2 = u^2 + 2as

Here,

Graph A shows that the velocity stays at 4m/s, it is moving with constant velocity.

Graph B shows that the velocity increases by the same amount each second, it is accelerating by the same amount each second (uniform acceleration).

Graph C shows that the velocity increases by a larger amount each second, the acceleration is increasing (non-uniform acceleration).

Since gradient=Δy/Δx i.e. y= velocity and x= time so, gradient = acceleration.

This graph shows that velocity is decreasing in one direction and increasing in opposite direction.