Question

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

Answer 1

Given :

➝ Mass of car = 30kg

➝ Initial velocity = 30kmph

➝ Final velocity = 60kmph

To Find :

⟹ Work done.

SoluTion :

➳ This question is completely based on the concept of work - energy theorem.

➳ According to WET,

$\bigstar\:\boxed{\bf{W=\Delta(KE)=\dfrac{1}{2}m(v^2-u^2)}}$

Where,

፨ W denotes work done

፨ m denotes mass

፨ v denotes final velocity

፨ u denotes initial velocity

✴ Conversion :

⇒ 1kmph = 5/18mps

⇒ 30kmph = 30×5/18 = 8.33mps

⇒ 60kmph = 60×5/18 = 16.67mps

$\dashrightarrow\tt\:W=\dfrac{1}{2}m(v^2-u^2)\\ \\ \dashrightarrow\tt\:W=\dfrac{30}{2}[(16.67)^2-(8.33)^2]\\ \\ \dashrightarrow\tt\:W=15\times (277.89-69.39)\\ \\ \dashrightarrow\tt\:W=15\times 208.5\\ \\ \dashrightarrow\boxed{\bf{W=3127.5J=3.1kJ}}$

Answer 2

Given ,

• Initial velocity (u)= 30 km/h or 8.33 m/s
• Final velocity (v) = 60 km/h or 16.66 m/s
• Mass of body (m) = 30 kg

We know that ,

The work energy theorem states that the change in kinetic energy is work done

$\boxed{ \sf{work \: done = \frac{1}{2} m( {(v)}^{2} - {(u)}^{2} ) }}$

Thus ,

$\sf \mapsto Work done = \frac{1}{2} \times 30( {(16.66)}^{2} - {(8.33)}^{2} ) \\ \\\sf \mapsto Work done = 15 \times (277.55 - 69.39) \\ \\ \sf \mapsto Work done = 15 × 208.1 \\ \\ \sf \mapsto Work done = 3121.5 \: \: joule$

$\sf \therefore \underline{The \: work \: done \: is \: 3121.5 \: J}$