Question

Example 11.4 What is the work to be done
to increase the velocity of a car from
30 km h- to 60 km h if the mass of
the car is 1500 kg?
​

Answer 1

Answer:

• Work done by body = 156250 J

Explanation:

Given:-

• Initial velocity of Car, u = 30 km/h
• Final velocity of Car, v = 60 km/h
• Mass of Car, m = 1500 kg

To find:-

• The Work done, W =?

Knowledge required:-

• Work-Energy Theorem

According to the work-energy theorem the work done is equal to the change in kinetic energy of the body.

       W = 1/2 m v² - 1/2 m u²

Where,

W = work done

m = mass of body

v = final velocity of body

u = initial velocity of body

Solution:-

Let us first convert the Initial and final velocities into m/s

→ u = 30 km/h = 30 × 5/18 = 25/3  m/s

→ v = 60 km/h = 60 × 5/18 = 50/3  m/s

Now, Using the work-energy theorem

→ W = 1/2 m v² - 1/2 m u²

→ W = 1/2 m ( v² - u² )

→ W = 1/2 × 1500 × [ (50/3)² - (25/3)² ]

→ W = 750 × [ 2500/9 - 625/9 ]

→ W = 750 × 1875/9

→ W =  156250 J

Therefore,

• The work done by body = 156250 Joules.

Answer 2

$\huge{\boxed{\rm{Question}}}$

What is the work to be done to increase the velocity of a car from 30 km/h to 60 km/h if the mass of the car is 1500 kg?

$\huge{\boxed{\rm{Answer}}}$

$\large{\boxed{\boxed{\sf{Given \: that}}}}$

• Initial velocity = 30 km/h

• Final velocity = 60 km/h

• Mass = 1500 kg

$\large{\boxed{\boxed{\sf{To \: find}}}}$

• Work doned.

$\large{\boxed{\boxed{\sf{Solution}}}}$

• Work doned = 156250 Joules.

$\large{\boxed{\boxed{\sf{We \: also \: write \: these \: as}}}}$

• Work doned as w.

• Mass as m.

• Final velocity as v

• Initial velocity as u

$\large{\boxed{\boxed{\sf{How \: to \: do \: this \: question}}}}$

$\large{\boxed{\boxed{\sf{Let's \: understand \: the \: concept \: 1st}}}}$

• This question says that the work to be done to increase the velocity of a car from 30 km/h to 60 km/h if the mass of the car is 1500 kg ; afterthat it says us to find the worked done.

$\large{\boxed{\boxed{\sf{How \: to \: do \: this \: question}}}}$

$\large{\boxed{\boxed{\sf{Let's \: see \: the \: procedure \: now}}}}$

• To solve this question 1stly we have to know some important information like work-energy theorm. Converting km/h into m/s we get results. Afterthat using it's formula we have to put the values afterthat we get our final result that is 156250 J. Hence, 156250 Joules is the work doned.

$\large{\boxed{\boxed{\sf{Compulsory \: to \: know}}}}$

Define work - energy theorem ?

Work - energy theorem This theorm states that the net work done by the forces on an object is equals to the change in it's kinetic energy.

Work - energy theorm's formula is given below ↝

W = ½ m v² - ½ m u²

Where,

• m means mass

• w as work done

• v as final velocity

• u as initial velocity

$\large{\boxed{\boxed{\sf{Full \: solution}}}}$

According to the question, firstly we have to find convert initial velocity and final velocity as m/s from km/h.

⇒u = 30 km/h

⇒30 × 5/18

⇒25/3 m/s

⇒v = 60 km/h

⇒v = 60 × 5/18

⇒v = 50/3 m/s

Now we have to use the formula to find the work - energy therom to solve this question putting the values according to this formula we get the following results

⇨W = 1/2m v² - 1/2 m u²

⇨W = 1/2m ( v²-u² )

⇨W = 1/2 × 1500 × [ (50/3)² - (25/3) ]²

⇨W = 750 × [ 2500/9 - 625/9 ]

⇨W = 750 × 1875/9

⇨W = 156250 Joules.

Hence, 156250 Joules is the work doned.