Question

At the moment t = 0 a particle starts moving along the x-axis so that its velocity projection varies as v_x = 35cosπtcm/s, where t is expressed in seconds. Find the distance that this particle covers during t = 2.80s after the start.

Answer 1

Obviously the motion law is of the from, is x = asinωt. and v_x  = ωacosωt.

comparing v_x = ωacosωt with v_x = 35cosπt, we get

As n = 5 is odd, like (4.7), we have to basically find the distance covered by the particle starting from the extreme position in the time interval 0.3s.

Thus from the eqn.