Question

A car of mass 1000 kg starts from rest and attains
the velocity of 10 m/s in 5 sec. Calculate the
work done by the normal reaction of the car.​

Answer 1

Given :

• Initial velocity, u = 0 m/s (starts from rest)
• Final velocity, v = 10 m/s
• Time taken, t = 5 seconds
• Mass of a car, m = 1000 kg

To find :

• Acceleration, a
• Force, F
• Distance, s
• Work done, W

According to the question,

⇒ v = u + at

Where,

• v = Final velocity
• u = Initial velocity
• a = Acceleration
• t = Time taken

⇒ 10 = 0 + a × 5

⇒ 10 - 0 = 5a

⇒ 10 = 5a

⇒ 10 ÷ 5 = a

⇒ 2 = a

• So,the acceleration is 2 m/s².

Now,

⇒ F = ma

Where,

• F = Force
• m = Mass
• a = Acceleration

⇒ F = 1000 × 2

⇒ F = 2000 N

• So, the force is 2000 Newton.

⇒ s = ut + ½ at²

Where,

• s = Distance
• u = Initial velocity
• a = Acceleration
• t = Time taken

⇒ s = 0 × 5 + ½ × 2 × 5 × 5

⇒ s = 0 + 25

⇒ s = 25 m

• So, the distance travelled is 25 meter.

So,

⇒ W = F × s

Where,

• W = Work done
• F = Force
• s = Distance

⇒ W = 2000 × 25

⇒ W = 50,000 J

• So, the work done by the car is 50,000 Joules.

Answer 2

$\Large\bf{\color{indigo}GiVeN,}$

• Mass of a car is 1000 kg.

• Car starts from rest.

$\longmapsto\:\:\bf\blue{Initial\:velocity\:(u)\:=\:0\:m/s\:}$

• In 5 seconds car attains the velocity of 10 m/s.

$\longmapsto\:\:\bf\pink{final\:velocity\:(v)\:=\:10\:m/s\:}$

$\longmapsto\:\:\bf\purple{Time\:(t)\:=\:5\:s\:}$

$\bf\orange{We\:know\:that,}$

$\red\bigstar\:\:{\pink{\boxed{\boxed{\bf{\green{v\:=\:u\:+\:a\:t}}}}}}$

$:\implies\:\:\bf{10\:=\:0\:+\:a\times{5}}$

$:\implies\:\:\bf{5a\:=\:10}$

$:\implies\:\:\bf{a\:=\:\dfrac{10}{5}\:}$

$:\implies\:\:\bf\purple{acceleration\:(a)\:=\:2\:m/s^2}$

$\bf\green{Again\:we\:know\:that,}$

$\pink\bigstar\:\:{\orange{\boxed{\boxed{\bf{\color{peru}Force\:(F)\:=\:mass\times{a}}}}}}$

$:\implies\:\:\bf{F\:=\:1000\times{2}}$

$:\implies\:\:\bf\blue{F\:=\:2000\:N}$

$\bf\pink{We\:know\:that,}$

$\purple\bigstar\:\:{\red{\boxed{\boxed{\bf{\color{olive}S\:=\:u\:t\:+\:\dfrac{1}{2}\:a\:t^2}}}}}$

$:\implies\:\:\bf{S\:=\:0\times{5}\:+\:\dfrac{1}{2}\times{2}\times{5^2}}$

$:\implies\:\:\bf\orange{S\:=\:25\:m}$

$\bf\red{Again\:we\:know\:that,}$

$\orange\bigstar\:\:{\green{\boxed{\boxed{\bf{\color{cyan}Work\:done\:(W)\:=\:F\:.\:S}}}}}$

$:\implies\:\:\bf{W\:=\:2000\times{25}}$

$:\implies\:\:\bf\green{W\:=\:50000\:J}$

$\Large\bold\therefore$ The work done by the normal reaction of the car is 50000 J.