Question

What is the difference between these 2 formulas?

1.) S=v/t
2.) S= ut + 1/2 at square

where s = distance

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Answer 1

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YOUR ANSWER...

$s = \frac{v}{t}$

This is the formula of displacement or you can say distance.

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

This is an equation of motion which shows the value of s with respect to t.

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Answer 2

Equations of motion
In studying the motion of objects it is often helpful to use an equation to work out the velocity, acceleration or the distance travelled.

We use the following letters to represent certain quantities:


Distance travelled s measured in metres (m)
Time taken t measured in seconds (s)
The velocity at the start (called initial velocity) u measured in m/s
The velocity at the end (called the final velocity) v measured in m/s
The acceleration of the object a measured in m/s2

1. Non accelerated motion – that is motion at a constant velocity


The area under the line of the velocity –time graph is the distance travelled by the object in the time t.

For example u = 20m/s and t = 300 s
Distance (s) = ut = 20 x 300 = 6000 m

The equation for non accelerated motion is:

Distance (s) = velocity (u or v) x time (t) s = vt

2. Accelerated motion
Acceleration (a) = [change in velocity]/time = [v-u]/t
or
a = [v-u]/t


Another version is: v = u + at



Distance travelled = area under the line = ut + ½ (v-u)t

But acceleration = (v-u)/t and so (v-u) = at therefore:

Distance travelled (s) = ut + ½ (v-u)t = ut + ½ [at]t = ut + ½ at2

s = ut + ½at2


If the object starts from rest u = 0, and so the equation becomes:

s = ½at2


Another useful equation is:

v2 = u2 + 2as

USING EQUATIONS
This section is designed to help you work out some of the problems using the equations of motion.

CONSTANT VELOCITY
1. s = vt

CONSTANT ACCELERATION
2. v = u + at
3. s = ut + ½at2
4. average velocity = [v + u]/2
5. v2 = u2 + 2as