Question

Velocity of a particle of mass 0.5kg depends on posiiton x as v= 5 (x)^3/2m/s Find the total WD on particle from x= 0 to x=2 m

Urgent kindly don't spam 100 poitns

Answer 1

Given:

• x= 0

Then :

$u = 5 \times {0}^{ 3 \div 2}$

$\purple{\bold{\implies \: u = 0}}$

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• x= 2m

$v = 5 \times {2}^{3 \div 2}$

$\implies \:v =5 \times \sqrt{8}$

$\purple{\bold{\implies \: v = 10 \sqrt{2} }}$

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Work done = Change in Kinetic Energy

$\implies \: w = \dfrac{1}{2} m( { v}^{2} - {u}^{2} ) \\ \implies \: w = \dfrac{1}{2} \times 0.5 \times ( {(10 \sqrt{2}) }^{2} - {0}^{2} ) \\ \implies \: w = \frac{1}{2} \times 0.5 \times 200$

$\red{\boxed{\bold{\large{ \implies \: w = 50}}}}$

Answer 2

w=∫Fdx

=∫  

0

5

​  

7−2x+3x  

2

dx

=[7x−  

2

2x  

2

 

​  

+  

3

3x  

2

 

​  

]  

0

5

​  

 

=[7x−x  

2

+x  

3

]  

0

5

​  

 

=[7×5−5  

2

+5  

3

]−[0−0+0]

=[35−25+125]−0

=135J

In this question, answer is 135 J not 70J