Question

A 43.0 cm diameter wheel accelerates uniformly from 86.0 rpm to 362.0 rpm in 3.1 s. How far (in meters) will a point on the edge of the wheel have traveled in this time? socratic.org

Answer 1

15.6 m

Step-by-step explanation:

d = diameter of the wheel = 43 cm = 0.43 m

r = radius of the wheel = (0.5) d = (0.5) (0.43) = 0.215 m

w₀ = initial angular velocity = 86 rpm = 9.01 rad/s

v₀ = initial linear speed = r w₀ = (0.215) (9.01) = 1.94 m/s

w = final angular velocity = 362 rpm = 37.91 rad/s

v = final linear speed = r w = (0.215) (37.91) = 8.15 m/s

t = time taken = 3.1 s

Using the equation

v = v₀ + at

8.15 = 1.94 + a (3.1)

a = 2 m/s²

d = distance traveled by a point at the edge of the wheel

Using the equation

d = v₀ t + (0.5) at²

d = (1.94) (3.1) + (0.5) (2) (3.1)²

d = 15.6 m