question_answer

The distance travelled by a particle moving in a straight line is found to be proportional to the square of the time elapsed. Is it moving with constant speed or constant acceleration? Explain

Answer:

                Given, \[\text{x}\propto {{\text{t}}^{\text{2}}}\]or \[\text{x}=\text{k}{{\text{t}}^{\text{2}}}\]where k is a constant of proportionality. speed/velocity of the particle, \[v=\frac{dx}{dt}=\frac{d}{dt}(k{{t}^{2}})\]= 2kt ...(i) and acceleration of the particle, a = \[\frac{dv}{dt}=\frac{d}{dt}\] (2kt) = 2k ....(ii) From (i) and (it) we note that acceleration of the particle is constant whereas the velocity of the particle depends upon the time.