Question

$\huge\color{silver}{Question}$
What is the work to be done to increase the velocity of a car from 30 km/h to 40 km mass of the car is 1500 kg?​

Answer 1

$\bold{Given :} \\ \\ = > Initial \: Velocity \: of \: Car ( u ) = 30 km/hr \\ \\ </p><p> = > Final \: velocity \: of \: Car ( v ) = 40 \: km/hr \\ \\ \bold{To \: find :} \\ \\ = > Work \: done \: to \: increase \: the \: velocity \\ \: of \: a \: car \: from \: 30 \: km/hr \: to \: 40 \: km \: \\ mass \: of \: the \: car \: is \: 1500 \: kg. \\ \\ \bold{Solution :} \\ \\ = > Work \: done = Change \: in \: Kinetic \: energy \\ \\ \bold{</p><p>Formula :} \\ \\ = > kinetic \: energy = \frac{1}{2}mv {}^{2} \\ \\ = > work \: done = Final \: Kinetic \: energy - Initial \: Kinetic \: energy \\ \\ = = > \frac{1}{2}mv {}^{2} - \frac{1}{2} </p><p>mu {}^{2} \\ \\ = = > \frac{1}{2} (1500 \times 40 \times 40) - \frac{1}{2}(1500 \times 30 \times 30) \\ \\ = = > 1500 \times 20 \times 40 - 1500 \times 15 \times 30 \\ \\ = = > 1500 \times 800 - 22500 \times 30 \\ \\ = = > 1200000 - 675000 \\ \\ = = > \bold{525000 \: Joules \: or \: 525 \: KJ \: }$

• Therefore work done is 525 KJ or 525000 J .

Answer 2

${\underline{\overline{\sf Answer}}$

☆ Given, Initial velocity of the car = 30 km/h

Final velocity of the car = 40 km/h

Mass of the car = 1500 kg

☆ We know that work done = Change in kinetic energy

Kinetic energy = $\sf\frac{1}{2}mv^2$

☆ Work done = Final kinetic energy – Initial kinetic energy

= $\sf\frac{1}{2}mv^2-\frac{1}{2}mu^2$

= $\sf(\frac{1}{2}\times1500\times40\times40)-(\frac{1}{2}\times1500\times30\times30)$

= $\sf(1500\times20\times40)-(1500\times15\times30)$

= $\sf(30000\times40)-(22500\times30)$

= $\sf{1200000-675000}$

= $\sf{525000}$

Hence, work done is 525000 J or 525 KJ

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Hope it helps :D