Question

A racecar travels around a circular track of radius 400 meters at constant speed. If the car's acceleration is 4 m/s2, what is its speed?

Answer 1

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:

`a=(v^2)/(r)`

Where:

`\begin{gathered} a=\text{ acceleration} \\ v=\text{ velocity} \\ r=\text{ radius} \end{gathered}`

We will solve for the velocity first by multiplying both sides by "r":

`ar=v^2`

Now we take the square root to both sides:

`\sqrt[]{ar}=v`

Now we plug in the values:

`\sqrt[]{(4(m)/(s^2))(400m)}=v`

Now we solve the operations:

`40(m)/(s)=v`

Therefore, the velocity of the car is 40 meters per second.