Question

$\huge\underline{\bf \orange{Question :}}$

A body of mass 1000kg travelling at a speed of 36km/h is brought to rest in 50s .The average retarding force on the body will be​

Answer 1

$\huge\sf\pink{Answer}$

☞ Force = -200 N

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$\huge\sf\blue{Given}$

✭ Mass (m) = 1000 kg

✭ Initial Velocity (u) = 36 km/h

✭ Final Velocity (v) = 0 m/s

✭ Time (t) = 50 sec

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$\huge\sf\gray{To \:Find}$

◈ Avg retardation force?

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$\huge\sf\purple{Steps}$

Do we shall first find the acceleration of the body, for that we may use the first equation of motion, i.e,

$\underline{\boxed{\sf v = u+at}}$

◕ v = 0 m/s

◕ u = 36 km/h = $\sf 36 \times \dfrac{5}{18}$ = 10 m/s

◕ t = 50 sec

Substituting the values,

➝ $\sf v = u+at$

➝ $\sf 0 = 10+50\times a$

➝ $\sf -10 = 50a$

➝ $\sf \dfrac{-10}{50} = a$

➝ $\sf \red{a = -0.2 \ m/s^2}$

So now that we have the accelerataion the body the regarding force will be given by,

$\underline{\boxed{\sf F = ma}}$

Substituting the values,

➳ $\sf F = ma$

➳ $\sf F = 1000 \times -0.2$

➳ $\sf \orange{F = -200 \ N}$

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Answer 2

Given :

• Mass (m) = 1000 kg
• Time (t) = 50 seconds
• Initial velocity (u) = 36 km/h
• Final velocity (v) = 0 m/s

To find :

• Average retarding force

According to the question,

At first we have to km/h into m/s

$\sf{ \bullet \: \frac{36 \times 1000}{60 \times 60} } = \cancel\frac{36000}{3600} {}^{ \: \: 10} = 10 \: ms {}^{ - 1} \orange \bigstar$

Now we will use the formula :

$\star \boxed{\sf \red{ v = u + at }}$

Now we have to put the value according to the formula,

$\sf { v = u + at }$

$\sf{ \: \: : \implies \: 0 = 10 + a(50) }$

$\sf{ \: \: : \implies -10 = 50a }$

$\sf{ \: \: : \implies \cancel\frac{ - 10}{50} {}^{ \: \: 0.2} = a}$

$\sf{ \: \: : \implies - 0.2\:ms {}^{ - 2} = a} \: \orange \bigstar$

Now we will calculate the retarding force :

$\star \boxed{ \sf \red{F = ma}}$

• F stands for Force
• m stands for Mass
• a stands for Acceleration

Now according to the formula,

$\sf{ \: \: : \implies \: 1000 \times - 0.2}$

$\sf{ \: \: : \implies \: - 200 \: N} \: \orange \bigstar$

So,the retarding force is -200 N..