Chapter 2: Accelerated Motion

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.

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