Question

what work to be done for increasing velocity of car from 20 to 50m/s of work. if the car's weight is 1000kg in

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Answer 1

$\LARGE{\bf{\underline{\underline{GIVEN:-}}}}$

• Initial velocity (u) = 20ms⁻¹
• Final velocity (v) = 50ms⁻¹.
• Weight of car (m) = 1000 Kg.

$\LARGE{\bf{\underline{\underline{TO:FIND:-}}}}$

• We need to find the work done.

$\LARGE{\bf{\underline{\underline{SOLUTION:-}}}}$

▣ We know that work done - change in kinetic energy. In other words:

$\star \boxed{\sf{\red{W=Final \ K.E. - Initial \ K.E.}}}$

$\leadsto \sf{\green{W=\dfrac{1}{2}mv^2- \dfrac{1}{2} mu^2 }}$

$\leadsto \sf{\green{W=\dfrac{1}{2}m(v^2- u^2) }}$

▣ Where:

• W - work.
• m - mass.
• u - Initial velocity.
• v - FInal velocity.

▣ Now, substitute the values.

$\sf \to W=\dfrac{1}{2} \times 1000 \times (50^2 - 20^2)$

$\to \sf W=500 \times (2500-400)$

$\leadsto \sf{\blue{W=1050000 \ J}}$

OR

$\leadsto \sf{\blue{W=1050 \ kJ}}$

Work done - 1050 kJ.

Formulas used:

$\boxed{\sf{\red{K.E.=\dfrac{1}{2}\times mass \times velocity ^2 }}}$

Some more formulas:-

Kinematic equations:

$\boxed{\substack{\displaystyle \sf v=u+at \\\\ \displaystyle \sf s=ut+\dfrac{1}{2}gt^2 \\\\ \displaystyle \sf 2as=v^2-u^2}}$

Potential energy formula:

$\boxed{\sf{\red{P.E.= mass \times acceleration \ due \ to \ gravity \times height}}}$

Mechanical energy formula:

$\boxed{\sf{\red{M.E.=\frac{1}{2} mv^2 + mgh}}}$

Answer 2

$\LARGE{\bf{\underline{\underline{GIVEN:-}}}}$

• Initial Velocity - 20ms⁻¹
• Final Velocity - 50ms⁻¹
• Mass - 1000 kg

$\LARGE{\bf{\underline{\underline{TO\:FIND\::-}}}}$

• The work to be done to increase the velocity of the car .

$\LARGE{\bf{\underline{\underline{ANSWER\::-}}}}$

W = $\sf\dfrac{1}{2}m\:(\:v² \:-\: u² \:)$

= $\sf\dfrac{1}{2}$m ( 50² - 20² )

= $\sf\dfrac{1}{2}$m ( 2500 - 400 )

= $\sf\dfrac{1}{2}$m × $\sf{2100}$

= $\sf\dfrac{1}{2}$m × $\sf{1000\:×\:2100}$

= $\sf{500\:×\:2100}$

$\leadsto \sf{\red{1050000\:J}}$

$\LARGE{\bf{\underline{\underline{CONCLUSION\::-}}}}$

∴ 1050000 J is the work to be done to increase the velocity of the car .