Question

how long will it take a force of 10 N to Stop mass of 2.5 kg which is moving at 20m/s​

Answer 1

Answer:

Therefore, the object will take 5 sec to stop a mass of 2.5 kg which is moving at 20m/s.

Answer 2

Given :

• Force = 10 N
• Mass = 2.5 kg
• Initial velocity = 20 m/s
• Final velocity = 0 m/s [ since the mass is bought at rest ]

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To find :

• Time at which the mass is bought at rest.

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Concept :

For this question we would solve by using the first kinematical equation which is as follows -

$\bf\dag~v~=~u~+~at$

where,

• v denotes final velocity
• u denotes initial velocity
• a denotes acceleration
• t denotes time taken

‎ Now for using this equation we need to calculate acceleration and we do know that -

$\dag\:F~=~m \times a$

$\bf\implies\:a~=~\frac{F}{m}$

where,

• a denotes acceleration
• F denotes force
• m denotes mass

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So we would calculate the acceleration first and then the time required.

Hope am clear lets solve !~

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Solution :

Calculating acceleration -

$\bf\:a~=~\frac{F}{m}$

Substituting the values

$\sf\implies\:a~=~\frac{10}{2.5}$

$\sf\implies\:a~=~\frac{10 \times 10}{25}$

$\sf\implies\:a~=~\frac{100}{25}$

$\sf\implies\:a~=~\cancel{\frac{100}{25}}$

$\sf\implies\:a~=~\cancel{\frac{20}{5}}$

$\bf\implies\:a~=~4~N$

Since v < u, so acceleration will have a negative sign.

$\bf\implies\:a~=~(-4~N)$‎

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Now calculating the time required by applying the kinematical equation -

$\bf\:~v~=~u~+~at$

Substituting the values

$\sf\implies\:~0~=~20~+~(-4) \times t$

$\sf\:oR\:20~-~4 \times t~=~0$

$\sf\implies\:20~-~4t~=~0$

$\sf\implies\:-4t~=~0-20$

$\sf\implies\:\cancel{-}4t~=~\cancel{-}20$

$\sf\implies\:4t~=~20$

$\sf\implies\:t~=~\frac{20}{4}$

$\sf\implies\:t~=~\cancel{\frac{20}{4}}$

$\small{\underline{\boxed{\mathrm{\implies\:t~=~5~sec}}}}$ $\bf\color{orange}{⋆}$

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Verification :

Plugging the values of v, u, a and t together in kinematical equation -

$\sf\to\:~v~=~u~+~at$

$\sf\to\:~0~=~20~+~(-4) \times 5$

$\sf\to\:~0~=~20~+~(-20)$

$\sf\to\:~0~=~20~-~20$

$\sf\to\:~0~=~0$

Hence Verified !~

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‎‎$\sf\therefore\:~The~time~taken~to~stop~the~mass~is~5~sec.$

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