Question

The angle θ through which a disk drive turns is given by θ(t)=a+bt−ct3, where a,b and care constants, t is in seconds, and θ is in radians. When t=0,θ=π/4rad and the angular velocity is 2.50 rad/s , and when 1.10 s , the angular acceleration is 1.40 rad/s2 .

Find a including their units.

Find including their units.
π/4rad/s2
π/2rad/s
π/4rad
π/4rad/s

Answer 1

The value for the constant a in the angular position function θ(t) = a + bt - ct3 is π/4 radians, found using the initial condition at t=0 of θ=π/4 rad.

Step-by-step explanation:

The position function for the angular position of the disk drive θ(t) = a + bt - ct3 is given, with a, b, and c being constants, t being time in seconds, and θ in radians. When t=0, θ=π/4 rad and the angular velocity is 2.50 rad/s. In order to find the constant a, we use the conditions given at t=0: θ(0) = a + b(0) - c(0)3 = a = π/4 rad. Therefore, the value for a is π/4 radians.