Question

what is the work to be done to increase the velocity of car from 30 h - 1 to 60 km h -1 if the mass of the car is 1500kg???????


​

Answer 1

Given :

Mass of the car = 1500kg

Initial velocity = 30km/hr

Final velocity = 60km/hr

To Find :

Work done to increase velocity of the car.

Solution :

❖ As per work-energy theorem, work done is always equal to change in kinetic energy.

Mathematically, W = k' - k

• W denotes work done
• k' denotes final kinetic energy
• k denotes initial kinetic energy

Kinetic energy of body of mass m moving at a velocity of v is given by, k = 1/2 mv²

• Initial velocity = 30km/hr

• 30 × 5/18 = 8.33m/s

• Final velocity = 60km/hr

• 60 × 5/18 = 16.67m/s

By substituting the given values;

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

$\sf:\implies\:W=\dfrac{1}{2}(1500)[(16.67)^2-(8.33)^2]$

$\sf:\implies\:W=750(277.89-69.39)$

$\sf:\implies\:W=750(208.5)$

$:\implies\:\underline{\boxed{\bf{\purple{W=156,375\:J=156.4\:kJ}}}}$

Answer 2

${\bold{\large{\sf{\underbrace{Question}}}}}$

What is the work to be done to increase the velocity of car from 30 km/h to 60 km/h ; if the mass of the car is 1500 kg.

${\bold{\large{\sf{\underbrace{Answer}}}}}$

${\bold{\large{\sf{\underline{Given \: that}}}}}$

❖ Initial velocity = 30 km/h

❖ Final velocity = 60 km/h

❖ Mass = 1500 kg

${\bold{\large{\sf{\underline{To \: find}}}}}$

❖ Work done.

${\bold{\large{\sf{\underline{Solution}}}}}$

❖ Work done = 156375 Joules

${\bold{\large{\sf{\underline{Understanding \: the \: question}}}}}$

❖ This question says that their is a car its mass is 1500 kg. It's initial velocity and final velocity is given as 30 km/h and 60 km/h respectively. Afterwards this question says that we have to find the work to be doned.

${\bold{\large{\sf{\underline{Knowledge \: required}}}}}$

❖ According to the work energy theorm's = Work doned is always equal to kinetic energy change. That's why mathematically using rule is, ${\bold{\sf{W \: = \: k^{1} \: - \: k}}}$

Where the values,

❉ ${\sf{W}}$ means work doned

❉ ${\sf{k^{1}}}$ means final kinetic energy.

❉ ${\sf{k}}$ means initial kinetic energy.

❖ Kinetic energy –

❖ ${\large{\green{\bf{\boxed{Kinetic \: energy \: = ½ \: mv^{2}}}}}}$

${\bold{\large{\sf{\underline{Using \: concept}}}}}$

❖ Work doned.

${\bold{\large{\sf{\underline{Using \: formulas}}}}}$

❖ ${\large{\green{\bf{\boxed{Work \: done \: = \: \frac{1}{2}m(v^{2} - u^{2}}}}}}$

${\bold{\large{\sf{\underline{Full \: solution}}}}}$

${\green{\bf{\boxed{Work \: done \: = \: \frac{1}{2}m(v^{2} - u^{2}}}}}$

${\green{\bf{\boxed{Work \: done \: = \: \frac{1}{2}(1500[(16.67)^{2} - (8.33)^{2}]}}}}$

${\green{\bf{\boxed{Work \: done \: = \: 750(277.89 \: - \: 69.39)}}}}$

${\green{\bf{\boxed{Work \: done \: = \: 750(208.5)}}}}$

${\green{\bf{\boxed{Work \: done \: = \: 750 \times 208.5}}}}$

${\green{\bf{\boxed{Work \: done \: = \: 156375 \: Joules}}}}$