Question

If a car is driving around a racetrack with a radius of 7 meters and has a centripetal acceleration of 72 m/s2, what is the velocity of the car?

Answer 1

Velocity: 22.44994432

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

We're given the radius, which is 7 meters, and the acceleration is 72

`a_c=(v^2)/(7)\\ 72=(v^2)/(7)`

Solve for v

Step 1: Simplify both sides of the equation.

72 = (1/7)v^2

Step 2: Subtract 1/7v^2 from both sides.

72 − (1/7)v^2 = (1/7)v^2 − (1/7)v^2

((−1)/7)v^2+72=0

Step 3: Subtract 72 from both sides.

((−1)/7)v2 + 72 − 72 = 0 − 72

((−1)/7)v^2= −72

Step 4: Divide both sides by (-1)/7.

((−1)/7)v^2 /(−1)/7 = −72 /(−1)/7

v^2=504

Step 5: Take square root.

v=±√504

v = 6√14 or v = −6√14

v = 22.4499443206 or -22.4499443206

-22.4499443206 wouldn't work for this, as -22.4499443206/7 = -72

V = 22.44994432

72 = 22.44994432^2/7

72 = 504/7

72 = 72