Question

Derive the equation of motion (Both the methods).​

Answer 1

Answer:

By using calculus

1). Acceleration is given as rate of change of velocity

$a = \frac{dv}{dt}$

Now on integrating both sides

a∫

0

t

dt=∫

u

v

dv

On solving the above we get

v=u+at

2). Rate of the displacement is equal to velocity

v=

dt

ds

On integrating the above equation we get

∫

0

s

ds=v∫

0

t

dt

On substituting the value ofv=u+at

We get

s=ut+

2

1

at

2

3). Distance travelled is equal to average speed time time

s=

2

u+v

t

By using the first equation and substituting the value oft=

a

v−u

We get

v

2

=u

2

+2as

Explanation:

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