Question

A particle moves along a straight line with an acceleration of a 5/(3 s¹/³ + s⁵/² ) m/s², where s is in meters. Part A Determine the particle's velocity when s = 2 m, if it starts from rest when s=1 m. Use a numerical method to evaluate the integral.

Answer 1

To determine the particle's velocity when s = 2 m, we can use numerical integration. We need to integrate the acceleration function with respect to time from s = 1 m to s = 2 m.

Step-by-step explanation:

To determine the particle's velocity when s = 2 m, we can use numerical integration. We need to integrate the acceleration function with respect to time from s = 1 m to s = 2 m.

We can use a numerical method like Simpson's rule or the trapezoidal rule to approximate the integral. Let's use the trapezoidal rule for simplicity.

The formula for the trapezoidal rule is:

∫[a,b]f(x)dx ≈ (b - a)/2 * [f(a) + f(b)]

Using this formula, we can calculate the approximate integral of the acceleration function over the given range and find the particle's velocity when s = 2 m.