# Formula of Dynamics

As all of us know dynamics teaches us about the motion of any body grounded on how the forces are exerted on it. Perhaps these equations were derived founded on experimenting with the motion.

There are four elementary equations in dynamics specifically,

$v=u+at$

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

$s=vt-\frac{1}{2}at^{2}$

$s=\frac{1}{2}(u+v)t$

$v^{2}=u^{2}+2as$

Where,

• u is initial velocity in m/s
• v is the final velocity in m/s
• s is theÂ distance traveled in m
• a is theÂ acceleration in m/s2
• t is the time taken in s

Dynamics FormulasÂ are valuable in computing the unfamiliar physical quantity when some of these quantities are known.

### Dynamics Solved Examples

Underneath are given some problems based on dynamics you can refer toÂ this while solving your assignment problems.

ProblemÂ 1:Â John throws a ball and it moves along the horizontal direction. If it travels a distance of 30 m in 2s. Calculate its acceleration.

Solution:

Known: u (Initial velocity) = 0,
s (Distance traveled) = 30 m,
t (Time taken) = 2 s

Distance travelled is given by

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

$30=0+\frac{1}{2}a(2^{2})$

$30=2a$

$Acceleration&space;a=15m/s^{2}$

Problem 2:Â  IfÂ and find the value of ‘‘, ifÂ ,Â ,Â

Solution:

Known: u (Initial velocity) = 0,
s (Distance traveled) = 150 m,
a (acceleration) = 3 m/s2

v2 = 0 + (2Ã—3Ã—150)

v2 = (2Ã—3Ã—150)

v2 = 900

Final velocity v =Â Â±30 m/s

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