question_answer

If the initial velocity of a particle is u and collinear acceleration at any time t is at, calculate the velocity of the particle after time t.

Answer:

                By definition, acceleration =\[\frac{\text{dv}}{\text{dt}}=\text{at }\] or \[\text{dv}=\text{at dt}\] Integrating it, we have \[\int\limits_{u}^{v}{dv}=\int\limits_{0}^{t}{at\,\,dt}\] or \[\text{v - u =}+\frac{1}{2}\text{a}{{\text{t}}^{\text{2}}}\] or \[\text{v }=\text{u}+\frac{1}{2}\text{a}{{\text{t}}^{\text{2}}}\].