Question

The velocity of a moving vehicle is given by the following equation = 5 (). (2 3)4 The task is to use the Chain Rule to determine an equation for the acceleration when = .

Answer 1

To use the Chain Rule to determine an equation for acceleration, differentiate the given velocity equation with respect to time. The equation for acceleration is a = 40μ(μ² + 3)³.

Step-by-step explanation:

To use the Chain Rule to determine an equation for acceleration, we need to differentiate the given velocity equation with respect to time. The given velocity equation is v = 5(μ² + 3)⁴.

Step 1: Differentiate the outer function. The derivative of (μ² + 3)⁴ with respect to μ is 4(μ² + 3)³.

Step 2: Multiply by the derivative of the inner function. The derivative of μ² + 3 with respect to μ is 2μ. So, the derivative of the entire equation is 5 * 4(μ² + 3)³ * 2μ = 40μ(μ² + 3)³.

Thus, the equation for acceleration is a = 40μ(μ² + 3)³.