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A single conservative force F(x) acts on...

A single conservative force `F(x)` acts on particle that moves along the x-axis. The graph of the potential energy with x is given. At `x = 5m`, the particle has a kinetic energyof `50 J` and its potential energy is related to position 'x' as `U = 15 + (x - 3)^(2)` Joule, where x is in mete then :

A

The mechanical energy of system is 69 J

B

The mechanical energy of system is 19 J

C

At `x = 3`, the kinetic energy of particle in minimum

D

the maximum value of kinetic energy is 54 J

Text Solution

Verified by Experts

The correct Answer is:
A, D
`U = 15 + (x - 3)^(2)`
`U = (5) = 19` & `KE (5) = 50`
Total mechanical energy `= 50 + 19 = 69J`
`U_("min") -= U (x - 3) = 15 J`
`KE_("max") = 69 - U_("min") = 69 - 15 = 54 J`
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