Answer to Question #239671 in Physics for Polen

Question

What must be the magnitude of the displacement of the automobile (from rest) after 7 seconds of travel if its velocity as function time is v(t) = 15t m/s along positive x-axis?

Answer 1

Let's first find the acceleration of the automobile:

$$a=\dfrac{dv}{dt}=\dfrac{d}{dt}(15t)=15\ \dfrac{m}{s^2}.$$

Finally, we can find the displacement of the automobile (from rest) after 7 seconds of travel from the kinematic equation:

$$d=v_0t+\dfrac{1}{2}at^2,$$ $$d=0+\dfrac{1}{2}\cdot15\ \dfrac{m}{s^2}\cdot(7\ s)^2=367.5\ m.$$