Question

Please answer ques
tion no 81

Answer 1

Answer:

5200J

Explanation:

v=dx/dt=2t+6t²

a=dv/dt=2+12t.....(i)

putting value t=2s in eq.(i) we get a=26

x=t²+2t³=4+16=20

w=m×a×x

=10×26×20

=5200J

My technique is right but given options are not matched.

I think options aren't right.

you should check this.

Answer 2

Answer:

Work Done = F.dx

According to the question,

Mass of the body is 10 kg. The distance is given as a function of time as:

x(t) = t² + 2t³

We know that, Force is mass times acceleration. Also we know that differential form of Acceleration in terms of x(t) is ( d²x/dt² )

Therefore Double differentiating x(t) we get,

⇒ ( d²x/dt² ) = 2 + 12t = a

We are now given with time to be 2 seconds. Substituting t = 2 in the above equation we get,

⇒ a = 2 + 12 ( 2 )

⇒ a = 2 + 24

⇒ a = 26 m/s²

⇒ Force = 10 × 26 = 260 N

⇒ Work Done =  260 × ( 2² + 2(2)³ )

⇒ Work Done = 260 × ( 4 + 16 )

⇒ Work Done = 260 × 20

⇒ Work Done = 5200 J

This is the required answer.