Aparticle travels on the x-axis so its velocity at time t is given by v(t)=1/2-cos(t) meters per second, where t is between 0 and 2pi, inclusive. a. for what values of t is the particle moving to the right? . b. if the particle starts at x=3, what is the final position of the article? . c. what is the total distance traveled by the particle? . d. when t=pi/4, is the speed of the particle increasing or decreasing?

3. a worker pushes a 30.5 kg polished stone along a polished table with a force on bonin a straight line for 5.20 s after starting from rest. there is no friction between thestone and the table. at the end of the table. the stone is hooked to a cable with a lengthof 62.0 cm to rotate it to a rough table to store until they can be picked up. the roughtable has a coefficient of static friction 0.702 with the polished stone. remember that 8= 9.80 m/s2a) what is the speed of the stone when it is hooked to the cable? b) what is the tension in the cable while the stone is rotating? (there is still nofriction)c) how much force is needed to make the stone begin sliding from rest on therough table? ius = 0.70262.0 cm30.5 kg20.5 kg6= 0