Question

To analyze the motion of a body that is traveling along a curved path, to determine the body's acceleration, velocity, and position. A motorcyclist travels around a curved path that has a radius of 250 ft . While traveling around the curved path, the motorcyclist increases speed by 1.05 ft/s2 . Part A - Finding the time interval for the motorcyclist to reach a given acceleration If the motorcyclist starts from rest, determine the time needed to reach an acceleration of 4.25ft/s2. Express your answer to three significant figures and include the appropriate units.

Answer 1

a^2 = ar^2 + al^2 where ar is the radial acceleration and al is the

linear acceleration - since vectors ar and al are at right angles

ar^2 = a^2 - al^2 = 4.25^2 - 1.05^2

ar = 4.12 ft/s^2

ar = V^2 / R where ar is the radial acceleration

So V^2 = ar * R = 4.12 * 250 = 1030 ft^2/s^2

V = 32.1 m/s the linear speed of the cycle

Also, V = al t or t = V / al = 32.1 / 1.05 = 30.6 sec