The time it takes for the cord to unwind is determined as 16.33 s.
How to calculate the time it will take the wheel to unwind?
The time it takes for the cord to unwind is calculated by applying the following formula as shown below.
θ = ω₀ + ¹/₂αt²
Where;
- ω₀ is the initial angular velocity (0 rad/s)
- α is the angular acceleration
- t is the time of motion
The angular displacement of the cord when it unwinds is;
θ = s / r
where;
- s is the distance traveled = 4 m
- r is the radius of the wheel = 3 cm / 2 = 1.5 cm = 0.015 m
θ = s / r
θ = 4 / 0.015
θ = 266.67 rad
The time it takes for the cord to unwind is calculated as;
θ = ω₀ + ¹/₂αt²
θ = 0 + ¹/₂αt²
θ = ¹/₂αt²
t = √ (2θ / α)
t = √ (2 x 266.67 / 2)
t = 16.33 s