Question

A 4 kg object at rest is subjected to a force (2i+6j)N. What is its velocity vector after after 2 sec

Answer 1

GiveN :

• Mass (m) = 4 kg
• F = (2i + 6j) N
• Time = 2s
• Initial velocity (u) = 0 m/s

To FinD :

• Velocity Vector

SolutioN :

⇒F = dp/dt

⇒Δp = F.dt

Integrate both sides

⇒∫Δp = ∫F.dt

⇒p = (2i +6j) * 2

⇒p = mv = (2i + 6j) * 2

⇒v = ((2i + 6j) * 2)/4

⇒v = (2i + 6j)/2

⇒v = (i + 3j) m/s

Answer 2

Answer:

• velocity vector of object = ( i + 3 j ) m/s

Explanation:

Given,

• Mass of object, m = 4 kg
• Force vector, F = ( 2i + 6j ) N
• Initial velocity of object, u = 0
• Time, t = 2 sec

To find,

• Velocity vector of object after time (t), v =?

Knowledge required,

• Newton's second law of motion

        F = m a

• First equation of motion

      v = u + a t

[ Where F is force, m is mass, a is acceleration, v is final velocity and t is time taken ]

Solution,

Using Newton's second law of motion

→ F = m a

→ a = F / m

→ a = ( 2 i + 6 j ) / ( 4 )

→ a = ( 0.5 i + 1.5 j ) m/s²

Now using first equation of motion

→ v = u + a t

→ v = ( 0 ) + ( 0.5 i + 1.5 j ) ( 2 )

→ v = (i + 3 j)  m/s  

Therefore,

• Velocity vector of object is ( i + 3 j ) m/s.