If a particle's kinetic energy increases from 8 J to 32 J, what is the total work done on the particle?

If a particle's kinetic energy increases from 8 J to 32 J, what is the total work done on the particle?

• A. -24 J
• B. 24 J
• C. 40 J
• D. 0 J

Answer: (B)

Work done on a particle equals the change in its kinetic energy. W = ΔK = K_f − K_i. With K_i = 8 J and K_f = 32 J, the change is 32 − 8 = 24 J. So the total work is +24 J, meaning energy was added to the particle by the forces. The other numbers don’t fit the situation: negative 24 J would mean the energy decreased, zero would mean no energy transfer, and 40 J would require an initial kinetic energy of -8 J, which isn’t the case here.

Work done on a particle equals the change in its kinetic energy. W = ΔK = K_f − K_i. With K_i = 8 J and K_f = 32 J, the change is 32 − 8 = 24 J. So the total work is +24 J, meaning energy was added to the particle by the forces. The other numbers don’t fit the situation: negative 24 J would mean the energy decreased, zero would mean no energy transfer, and 40 J would require an initial kinetic energy of -8 J, which isn’t the case here.