Question

A box with a mass of 15 kg is pushed with a net force of 180 N. What magnitude of acceleration will the box experience?

Answer 1

`\tt {\pink{Given}}\begin{cases} \sf{\green{Force=180 \: newtons}}\\ \sf{\blue{Mass=15 \: kg}}\\ \sf{\orange{Acceleration= \: ?}}\end{cases}`

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Answer:

`\qquad \: \tiny\dag\:\underline{\tt By \: applying \: Newtons \: second \: law \: of \: motion \: we \: get : } \\ \\`

`:\implies\sf F = ma \\ \\`

`\tt {\pink{Where}}\begin{cases} \sf{\green{F=Force}}\\ \sf{\blue{m=Mass}}\\ \sf{\orange{a=Acceleration}}\end{cases}`

• This law states that, "the rate of change of momentum of a body is directly proportional to the external force applied on the body and the change takes place in the direction of applied force" :]

`\qquad\tiny\dag\:\underline{\tt Now,substituting\: the \: given \: values \: in \: above \: Formula \: we \: get :} \\ \\`

`:\implies\sf 180 = 15 * Acceleration \\ \\ \\`

`:\implies\sf Acceleration = (180)/(15) \\ \\ \\`

`:\implies \underline{ \boxed{\textsf{ \textbf{ Acceleration = 12 m/s$^2$ }}}} \\ \\ \\`

`\therefore\underline{\textsf{ Acceleration produced by the box is \textbf{12 m/s$^2$}}}. \\`

Answer 2

`\huge{ \underline{ \underline{ \red{ \bf{Solution:}}}}}`

We know that, Newton's second law of motion states that Force is the product of mass and Accleration which is actually derived from the original statement, Rate of change of momentum is directly proportional to Force applied and acts in the same direction of force.

According to this,

`\large{ \cdot{ \boxed{ \rm{f = m * a}}}}`

Where,

• F = Force applied
• m = mass of the body
• a = acceleration of the body

So, By using formula,

➝ F = m × a

➝ 180 N = 15 kg × a

➝ 15a = 180

➝ a = 180/15 = 12 m/s²

❍ Accleration of the body = 12 m/s²

Hence, solved !!

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