Question

The velocity acquired by a body moving with uniform acceleration is 12m/s in 2s and 18m/s in 4 s. find the initial velocity of the body.

Answer 1

AnswEr :

• Initial velocity of body is 6 m/s

ExplanaTion :

Let, initial velocity of body be u and

uniform acceleration of body be a

Now,

As we know First equation of motion

• v = u + a t

[ where v is taken as final velocity, u is taken as initial velocity, a is taken as acceleration and t is time taken ]

Considering Case (1)

• when Body acquires a velocity of 12 m/s in 2 seconds

then,

taking, initial velocity = u

acceleration = a

final velocity  = 12 m/s

time taken = 2 sec

Using first equation of motion

→ v = u + a t

→ 12 = u + a (2)

→ 12 = u + 2 a

→ 2 a = 12 - u

→ a = ( 12 - u ) / 2   _____equation (1)

Considering Case (2)

• when body acquires a velocity of 18 m/s in 4 sec with same acceleration and initial velocity as in case (1)

then,

taking, initial velocity = u

acceleration = a

final velocity = 18 m/s

time taken = 4 sec

Using first equation of motion

→ v = u + a t

→ 18 = u + a (4)

→ 18 = u + 4 a

→ 4 a = 18 - u

using equation (1) substituting value of a

→ 4 ( 12 - u )/2 = 18 - u

→ 2 ( 12 - u ) = 18 - u

→ 24 - 2 u = 18 - u

→ 24 - 18 = 2 u - u

→ u = 6 m/s

therefore,

• Initial velocity of body is 6 m/s .