Question

a force of 2nd acting on a body changes its velocity uniformly form 2m/so to 5m/s in 10s calculate the mass of the body

Answer 1

Given,

Initial velocity ( u ) = 2 m/s

Final velocity ( v ) = 5 m/s

Time ( t ) = 10 s

Acceleration ( a ) = ?

Using 1st equation of Motion,

⇒v = u + at

⇒ 5 m/s = ( 2 m/s ) + a( 10 s )

⇒ ( 5 m/s ) - ( 2 m/s ) = 10 as

⇒ 3 m/s = 10 as

⇒ ( 3 m / 10 s × s ) = a

⇒ 0.3 m/s² = a

•°• a = 0.3 m/s²

Now,

Given,

Force applied = 2 N

Using formula,

⇒ Force = Mass × Acceleration

⇒ 2 N = Mass × 0. 3 m/s²

⇒ 2 kg m/s² = Mass × 0.3 m/s²

⇒ ( 2 kg m/s² ) ÷ ( 0.3 m/s² ) = Mass

⇒ ( 2 kg / 0.3 ) = Mass

⇒ ( 20 kg / 3 ) = Mass

•°• Mass = 20 kg / 3 = 6.67 kg ( Approx. )

Answer 2

Given :

• Force (F) = 2 N

• Initial velocity (u) = 2 m/s

• Final velocity (v) = 5 m/s

• Time interval (t) = 10 s

To Find :

• Mass of the body

Solution :

Use 1st equation of motion for calculating value of acceleration :

$\\ \implies \boxed{\rm{v = u + at}} \\ \\ \\ \implies \rm{a = \dfrac{v - u}{t}} \\ \\ \\ \implies \rm{a = \dfrac{5 - 2}{10}} \\ \\ \\ \implies \rm{a = \dfrac{3}{10}} \\ \\ \\ \implies \rm{a = 0.3} \\ \\ \\ \underline {\rm{\therefore \: Acceleration \: of \: body \: is \: 0.3 \: ms^{-2}}}$

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Now, use formula of force

$\implies \boxed{\rm{F = ma}} \\ \\ \\ \implies \rm{m = \dfrac{F}{a}} \\ \\ \\ \implies \rm{m = \dfrac{2}{0.3}} \\ \\ \\ \implies \rm{m = 6.67} \\ \\ \\ \underline {\rm{\therefore \: Mass \: of \: body \: is \: 6.67 \: kg}}$