Question

Calculate the time needed for a net force of 5n to change the velocity of a 10kg of mass by 2m/s is

Answer 1

Given,

• Force applied, $\sf{F=5\ N}$

• Mass of the body, $\sf{m=10\ kg}$

• Change in velocity due to the force, $\sf{\Delta v=2\ m\,s^{-1}}$

• The time needed for the force to change the velocity $\sf{=\Delta t\quad (Say)}$

The change in momentum of the body due to the force is,

$\displaystyle\longrightarrow\sf{\Delta p=m\cdot\Delta v}$

$\displaystyle\longrightarrow\sf{\Delta p=10\times2}$

$\displaystyle\longrightarrow\sf{\Delta p=20\ N\,s}$

By Newton's Second Law of Motion, we have,

$\displaystyle\longrightarrow\sf{F=\dfrac{\Delta p}{\Delta t}}$

Then,

$\displaystyle\longrightarrow\sf{\Delta t=\dfrac{\Delta p}{F}}$

$\displaystyle\longrightarrow\sf{\Delta t=\dfrac{20}{5}}$

$\displaystyle\longrightarrow\sf{\underline{\underline{\Delta t=4\ s}}}$

Hence the force needed 4 seconds to change the velocity of the body by $\sf{2\ m\,s^{-1}.}$

Answer 2

Solution :

⏭ Given:

• Net force applied on body = 5N
• mass of body = 10kg
• Change in velocity = 2mps

⏭ To Find:

• Time needed to change the velocity of body

⏭ Formula:

✏ As per Newton's second law of motion

$\bigstar \: \boxed{ \tt{ \pink{ \large{F \times \triangle{t} = \triangle{P}}}}} \: \bigstar$

⏭ Terms indication:

• F denotes applied force
• Δt denotes time interval
• ΔP denotes change in momentum

⏭ Calculation:

$\twoheadrightarrow \sf \: F \times \triangle{t} = m \times \triangle{v} \\ \\ \twoheadrightarrow \sf \: 5 \times \triangle{t} = 10 \times 2 \\ \\ \twoheadrightarrow \sf \: \triangle{t} = \frac{20}{5} \\ \\ \twoheadrightarrow \: \boxed{ \tt{ \purple{ \large{ \triangle{t} = 4 \: sec}}}}$

⏭ Additional information:

• Momentum is a vector quantity.
• Vector quantity has both magnitude as well as direction.