Question

The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 5 sin(πt) + 5 cos(πt), where t is measured in seconds. (Round your answers to two decimal places.) (a) Find the average velocity during each time period. g

Answer 1

The particle has a displacement of 375 m at t = 5 s, with a velocity of 180 m/s. Average velocity is found by dividing net displacement by the total time.

Step-by-step explanation:

The displacement of a particle at t = 5 seconds with an initial velocity of 30 m/s and a constant acceleration of 30 m/s2 is given by the equation s = ut + (1/2)at2, where u is the initial velocity and a is the acceleration. Plugging in the values, we get s = (30 m/s)(5 s) + (1/2)(30 m/s2)(5 s)2, resulting in a displacement of 375 m. The velocity at the same time, calculated using the equation v = u + at, is 180 m/s. To find the average velocity during a time period, the net displacement is divided by the total time. For example, if a particle's net displacement is 2,700 m over a period of 30 seconds, its average velocity is 2,700 m / 30 s = 90 m/s.