Question

A car is traveling at a constant speed on the highway. Its tires have a diameter of 61.0 cm and are rolling without sliding or slipping. If the angular speed of the tires is 50.0 rad/s, what is the speed of the car

Answer 1

15.25 m/s

Step-by-step explanation:

Speed: This can be defined as the rate of change of distance. The S.I unit of speed is m/s.

The expression of speed in terms of angular speed is given as

v = rω..................... Equation 1

Where v = speed of the car, ω = angular speed of the tires, r = radius of the tires

Given: ω = 50 rad/s, r = d/2 = where d = diameter of the tire, d = 61 cm

r = 61/2 = 30.5 cm = 0.305 m.

Substitute into equation 1

v = 50(0.305)

v = 15.25 m/s.

Hence the speed of the car = 15.25 m/s

Answer 2

15.25 m/s

Step-by-step explanation:

Velocity is given as;

v = angular velocity x radius

v = ωr

where;

v is velocity, ω = angular velocity and r is radius)

We are given;

ω = 50 rad/s

diameter = 61cm

So, radius = 61/2 = 30.5 cm = 0.305m

Plugging in the relevant values to get ;

v = 50 x 0.305

v= 15.25 m/s

Therefore the car is travelling at a constant speed of 15.25 m/s