Question

What is the work to be done to increase the velocity of a car from 30m/s to 60m/s if the mass of the car is 1500kg.

Answer 1

AnswEr:

• The Work done (W) is 2.025 Mega Joules

Given:

1. Initial velocity (u) = 30 m/s.
2. Final velocity (v) = 60 m/s.
3. Mass of Car (M) = 1500 Kg.

Explanation:

$\rule{300}{1.5}$

From work energy theorem we know,

$\large\bigstar\: \underline{\boxed{\sf W = \dfrac{1}{2}\:M\: \bigg(v^2 - u^2\bigg)}}$

Here,

• M Denotes Mass of car.
• v Denotes final velocity.
• u Denotes initial velocity.

Substituting the values,

$\longrightarrow\sf W = \dfrac{1}{2}\times 1500\times \bigg((60)^2 - (30)^2\bigg)\\\\\\\longrightarrow\sf W = 750 \times \bigg(3600 - 900\bigg)\\\\\\\longrightarrow\sf W = 750 \times 2700 \\\\\\\longrightarrow\sf W = 2025000\\\\\\\longrightarrow\sf W = 2.025 \times 10^{6}$

• 10⁶ = Mega prefix.

Solving,

$\longrightarrow\sf W = 2.025 \: MJ \\\\\\\longrightarrow\large{\underline{\boxed{\red{\sf W = 2.025 \: MJ}}}}$

∴The Work done (W) is 2.025 Mega Joules.

$\rule{300}{1.5}$

Answer 2

$\boxed{\underline{\bold{\bf{\blue{W=\frac{1}{2}m(v^2-u^2)}}}}}$

where ,

• W denotes work done
• m denotes mass of the object
• v denotes final velocity
• u denotes initial velocity

Given ,

Work to be done = ?

Initial velocity , u = 30 m/s

Final velocity , v = 60 m/s

Mass of the car , m = 1500 kg

$\bold{W=\frac{1}{2}m(v^2-u^2) }\\\\\implies \bold{W=\frac{1}{2}(1500)(60^2-30^2) }\\\\\implies \bold{W=(750)(3600-900)}\\\\\implies \bold{\bf{\red{W=20,25,000\ Joules}}}\\\\\implies \bold{\bf{\red{W=2.025\ M\ Joules}}}$

So the work  to be done to increase the velocity of a car from 30 m/s to 60 m/s having mass of 1500 kg is 2.025 Mega Joules