Answer to Question #172473 in Classical Mechanics for Jethro Torio

Question

Starting from rest a car attains an acceleration of 2 m/s^-2

Find the time and velocity at this position. (in km/hr)

Answer 1

Unfortunately, from the condition of the question we don't know the position of the car. Let's assume that the car attains an acceleration of 2 m/s^-2 at position $d=10\ m$. Then, we can find the time that the car takes to accelerate from the formula:

$$d=v_0t+\dfrac{1}{2}at^2,$$ $$d=\dfrac{1}{2}at^2,$$ $$t=\sqrt{\dfrac{2d}{a}}=\sqrt{\dfrac{2\cdot10\ m}{2\ \dfrac{m}{s^2}}}=3.16\ s.$$

Finally, we can find the velocity at this position:

$$v=v_0+at,$$ $$v=0+2\ \dfrac{m}{s^2}\cdot3.16\ s=6.32\ \dfrac{m}{s}\cdot(\dfrac{1\ km}{1000\ m})\cdot(\dfrac{3600\ s}{1\ h})=22.75\ \dfrac{km}{h}.$$