Question

A particle is acted upon by a force F which varies with position x as shown in figure. If the particle at x = 0 has kinetic energy of J, then the kinetic energy of the particle at x = 16 m is:

• A. 45J
• B. 30 J
• C. 70 J
• D. 20 J

Answer 1

Answer: (A)

45J

Answer 2

Work done W = Area under f-x graph with proper sign

W = Area of triangle ABC + Area of rectangle CDEF+

Area of rectangle FGHI + Area of rectangle IJKL

$\mathrm { W } = \left[ \frac { 1 } { 2 } \times 6 \times 10 \right] + [ 4 \times ( - 5 ) + [ 4 \times ( 5 ) ] + 2 \times ( - 5 ) ]$

= 30 – 20 +20 -10

= 20J ……(i)

According to work energy theorem

$\mathrm { k } _ { \mathrm { f } } - \mathrm { f } _ { \mathrm { i } } = \mathrm { w }$

Or

$\left( \mathrm { K } _ { \mathrm { f } } \right) _ { \mathrm { x } = 16 \mathrm {~m} } = \left( \mathrm { k } _ { \mathrm { i } } \right) _ { \mathrm { x } = 0 \mathrm {~m} } + \mathrm { W }$

=25 J + 20 J

= 45 J