We are given that a car travels in a circular motion with an acceleration of 4m/s^2. We are asked to determine the speed of the motion. To do that we will use the following formula:
[tex]a=\frac{v^2}{r}[/tex]Where:
[tex]\begin{gathered} a=\text{ acceleration} \\ v=\text{ velocity} \\ r=\text{ radius} \end{gathered}[/tex]We will solve for the velocity first by multiplying both sides by "r":
[tex]ar=v^2[/tex]Now we take the square root to both sides:
[tex]\sqrt[]{ar}=v[/tex]Now we plug in the values:
[tex]\sqrt[]{(4\frac{m}{s^2})(400m)}=v[/tex]Now we solve the operations:
[tex]40\frac{m}{s}=v[/tex]Therefore, the velocity of the car is 40 meters per second.
