Question

Derive the derivative
(v=u+at)​

Answer 1

(a) Consider a body having initial velocity 'u'. Suppose it is subjected to a uniform acceleration 'a' so that after time 't' its final velocity becomes 'v'. Now, from the definition of acceleration we know that:

Acceleration =

Time taken

Change in velocity

or Acceleration =

time taken

Final velocity- Initial velocity

So, a=

t

v−u

at=v−u

and, v=u+at

where v= final velocity of the body

u= initial velocity of the body

a= acceleration

and t= time taken

(b) Initial velocity, u=54km/h=15m/s

Final velocity, v=0m/s

Time, t=8s

Acceleration, a=?

a=

t

v−u

=

8

0−15

=

8

−15

m/s

2

=−1.875m/s

Answer 2

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Explanation:

(a) Consider a body having initial velocity 'u'. Suppose it is subjected to a uniform acceleration 'a' so that after time 't' its final velocity becomes 'v'. Now, from the definition of acceleration we know that:

Acceleration =

Time taken

Change in velocity

or Acceleration =

time taken

Final velocity- Initial velocity

So, a=

t

v−u

at=v−u

and, v=u+at

where v= final velocity of the body

u= initial velocity of the body

a= acceleration

and t= time taken

(b) Initial velocity, u=54km/h=15m/s

Final velocity, v=0m/s

Time, t=8s

Acceleration, a=?

a=

t

v−u

=

8

0−15

=

8

−15

m/s

2

=−1.875m/s