A body of mass 2.5 kg which is at rest acquires a speed of 10 m/s when pushed forward. The impulse given is:

CONCEPT:

Impulse:

• A large force acting for a short time to produce a finite change in momentum is called impulse.
• The product of force and time is called an impulse of force.

\(\Rightarrow I=FΔ t\)

Where I = impulse, F = applied force and Δt = time

Newton's second law of motion:

• According to Newton's second law of motion, the rate of change of momentum of a body is directly proportional to the applied unbalanced force.
• The magnitude of the force is given as,

\(\Rightarrow F=\frac{Δ P}{Δ t}\)

Where ΔP = change in momentum

CALCULATION:

Given m = 2.5 kg, u = 0 m/s and v = 10 m/s

Where m = mass, u = initial velocity and v = final velocity

• The impulse is given as,

\(\Rightarrow I=FΔ t\)     -----(1)

• By Newton's second law of motion,

\(\Rightarrow F=\frac{Δ P}{Δ t}\)     -----(2)

By equation 1 and equation 2,

\(\Rightarrow I=\frac{Δ P}{Δ t}\times\Delta t\)

\(\Rightarrow I=Δ P\)     -----(3)

• The change in momentum is given as,

\(\Rightarrow Δ P=m(v-u)\)

\(\Rightarrow Δ P=2.5(10-0)\)

\(\Rightarrow Δ P=25\,Ns\)     -----(4)

By equation 3 and equation 4,

\(\Rightarrow I=25 \,Ns\)

Hence, option 4 is correct.