The angle through which a rotating wheel has turned in time t is given by \theta = a t - b t^2+ c t^4, where \theta is in radians and t in seconds.
Where is the question?
To find the angle through which a rotating wheel has turned in time t, we can use the given equation:
θ = at - bt^2 + ct^4
Here's how we can find the angle using this equation:
1. Identify the coefficients:
- a: coefficient of the term 't' (linear term)
- b: coefficient of the term 't^2' (quadratic term)
- c: coefficient of the term 't^4' (quartic term)
2. Plug in the values for a, b, and c.
3. Substitute the value of t into the equation.
For example, let's say a = 2, b = 0.5, c = 0.1, and t = 5. We can calculate the corresponding angle using the equation:
θ = (2 × 5) - (0.5 × 5^2) + (0.1 × 5^4)
Now, let's solve the equation step by step:
θ = (2 × 5) - (0.5 × 5^2) + (0.1 × 5^4)
= (2 × 5) - (0.5 × 25) + (0.1 × 625)
= 10 - 12.5 + 62.5
= 60 radians
Therefore, when t = 5 seconds, the angle through which the rotating wheel has turned is 60 radians.