Final answer:
The SI units for the constant k in the potential energy function U(r) = kr are joules per meter (J/m), as it is the constant that when multiplied by the distance r in meters gives the potential energy in joules.
Step-by-step explanation:
When we have a particle with potential energy depending on its distance r from the origin by the equation U(r) = kr, we're discussing a physics scenario, specifically relating to work and energy. The variable k in this equation represents a proportionality constant. To determine the SI units of k, we must consider the equation for potential energy (U) and the dimensions of each variable. Potential energy is measured in joules (J) in the SI unit system, and distance r is measured in meters (m).
The potential energy equation given is U(r) = kr, which implies that k * r should have units of joules (J). Since r is in meters (m), for the equation to be dimensionally consistent, k must have units of joules per meter (J/m), as it's the constant of proportionality that when multiplied by meters gives joules.