The velocity v of a particle of mass m at time t is given by the equation v = (1 - e^ - t m ) , where and are dimensional constants. The dimensions of represent the physical quantity

Step-by-step solution

The argument of an exponential function must be dimensionless. Therefore, the dimension of t m is 1 . [ t m ] = [M^0L^0T^0] [ ] = [m] [t] = [M] [T] = [MT⁻¹] By the principle of dimensional homogeneity, the prefactor must have the dimensions of velocity. [ ] = [v] = [LT⁻¹] [ ] = [v][ ] = [LT⁻¹][MT⁻¹] = [MLT⁻²] The dimensional formula [MLT⁻²] corresponds to force. Answer: force