Question

A force is applied on a body of mass 20 kg moving with a velocity of 40 ms-1. The body attains a velocity of 50 ms-1 in 2 seconds. Calculate the work done by the body.​

Answer 1

Given :

• Mass of a body = 20 kg
• Initial velocity of the body = 40 m/s
• Final velocity of the body = 50 m/s
• Time = 2 seconds

To find :

• Work done by the body

Concept :

To calculate the work done by the body, firstly we will calculate the acceleration and distance travelled by the body.

To calculate the acceleration we will use the first equation of motion. Then by using the third equation of motion we will find the value of distance travelled.

Solution :

Using first equation of motion,

• v = u + at

where,

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

Substituting the given values :-

⇒ 50 = 40 + (a)(2)

⇒ 50 - 40 = 2 × a

⇒ 10 = 2 × a

⇒ 10/2 = a

⇒ 5 = a

Acceleration of the body = 5 m/s²

Now, we will calculate the distance travelled :-

Using the third equation of motion,

• v² - u² = 2as

where,

• v denotes the final velocity
• u denotes the initial velocity
• a denotes the acceleration
• s denotes the distance

Substituting the given values :-

⇒ (50)² - (40)² = 2 × 5 × s

⇒ (50 - 40)(50 + 40) = 10 × s

⇒ 10 × 90 = 10 × s

⇒ 900 = 10 × s

⇒ 900/10 = s

⇒ 90 = s

The distance travelled by the body = 90 m

Now, we will calculate the force :-

Using formula,

• Force = ma

where,

• m denotes the mass
• a denotes the acceleration

Substituting the given values :-

⇒ Force = 20 × 5

⇒ Force = 100 N

Work done by the body :-

Using formula,

• W = F × s

where,

• W denotes the work
• F denotes the force
• s denotes the distance

Substituting the given values :-

⇒ Work = 100 × 90

⇒ Work = 9000

Therefore, the work done by the body = 9000 J

Answer 2

$\boxed{\Large\bf\red{ANSWER :- 9000 J}}$

$\bf\huge\underline{\underline{ Given :- }}$

• a force is applied to a body

• mass , m = 20 kg

• initial velocity , u = 40 m/s

• final velocity , v = 50 m/s

• time , t = 2s

$\bf\huge\underline{\underline{ To \: Find:- }}$

• Work done

$\bf\huge\underline{\underline{ Formulas \: used :- }}$

• $\boxed{\bf\red{a = \frac{v - u}{t} }}$

• $\boxed{ \bf\red{F = m a }}$

• $\boxed{\bf\red{ v² = u² + 2as }}$

$\bf\huge\underline{\underline{ Answer :- }}$

ACCELERATION

• $\boxed{\bf\red{a = \frac{v - u}{t} }}$

• $\red{\implies} \bf a = \frac{50 - 40}{2}$

• $\red{\implies}\bf a = \frac{10}{2}$

• $\red{\implies}\bf\pink{ a = 5 m/s² }$

$\rule{15cm}{0.02cm}$

FORCE

• $\boxed{ \bf\red{F = m a} }$

• $\red{\implies} \bf F = 20 × 5$

• $\red{\implies} \bf\pink{F = 100 N }$

$\rule{15cm}{0.02cm}$

DISPLACEMENT

• $\boxed{\bf\red{ v² = u² + 2as }}$

• $\red{\implies} \bf 50² = 40² + 2 × 5 × s$

• $\red{\implies} \bf s = \frac{2500 - 1600}{10} m$

• $\red{\implies}\bf\pink{ s = 90 m}$

$\rule{15cm}{0.02cm}$

WORK

• $\boxed{\bf\red{ W = F . d }}$

• $\red{\implies} \bf W = 100 × 90$

• $\red{\implies} \bf\pink{ W = 9000 J}$

$\rule{15cm}{0.02cm}$

So the Work Done by the body = 9000 J