Question

Im having trouble with all parts a-e

The tire of an accelerating car rotates with an angular velocity given by the equation omega(t) = A + Bt^2 where A and B are constants. At t = 0 seconds, the angular velocity is 4 rad/s, and at t = 3 seconds, the angular velocity is 22 rad/s. The radius of the tire is 0.25 meters. Solve for the constants A and B. Find an equation for the angular acceleration of the tire as a function of time (i.e. alpha(t) ) What is the angular displacement of the tire after 1 second If the tire is not slipping, what is the distance the car has travelled after 1 second What is the velocity of the car after 2 seconds

Answer 1

Solution: Given ω(t)--A + Bt2 Apply initial conditions At t-0, ω(t)-4 rad / sec At t-3, ω(t) =22 rad /sec 4 = A + B(0)2 A 9B 22 4 + 9B = 22 9 B18 Angular Acceleration α--aE-0 + 2Bt Angular Acceleration α--4t a(1) = 4 rad/s? dt dt - (4 2t2)0.25 -10.5t2 Velocity of car after 2 sec v 1 0.5(2)2 3 m/s