Question

The initial velocity of a body is 100cm/s.It has
a retardation of 5cm/second square. Find out the
velocity of the body after 15sec. Also, find out the
time which is required for the rest condition of the
object.​

Answer 1

Here,

Initial velocity ( u ) = 100 cm / sec.

Retardation ( - a ) = - 5cm / sec^2.

{ Retardation means negative acceleration }

Time ( t ) = 15 sec.

Final velocity ( v ) = ?

So, we know from the formula,

Acceleration = (Final velocity - Initial velocity)÷ Time.

i.e. a = ( v- u ) / t .

-5 = ( v - 100 ) / 15

-5 × 15 = v- 100.

{ transposing 15 to LHS }

- 75 = v - 100.

-75 + 100 = v

{ transposing -100 to LHS }

v = 25 cm/sec.

Therefore ,

'v' i.e. final velocity = 25cm/sec.

Now, we need to find the time at which the body comes to rest.

Here,

u = 25 cm/sec. { because the body is now going to be at rest , hence the final velocity becomes the initial velocity }

v = 0 cm / sec . { the body is at rest , hence no movement } .

acceleration = -5cm / sec^2.

Again , from the formula,

a = ( v - u ) / t

-5 = ( 0 - 25 ) / t.

-5 = -25 / t.

-5t = -25

t = -25 / -5.

t = 5 sec.

Hence , the body will come at rest in 5 seconds.