Question

Derive the relationship. F = m( v - u ) / t , where each symbol has its usual significance.

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Answer 1

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

= −15 m/s 2

=−1.875m/s 2

Answer 2

Answer:

(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 takenChange in velocity

or Acceleration = time takenFinal velocity- Initial velocity

So, a= tv−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= tv− = 80−15

8−15 m/s 2 =−1.875m/s 2