PLEASE HELP AND EXPLAIN

A particle moves along the x-axis so that its velocity at anytime is t greater than or equal to 0 is given by v(t)=1-sin(2pi t)
a) find the acceleration a(t) of the particle at any time.
b) find all values of t, 0

Question

PLEASE HELP AND EXPLAIN

A particle moves along the x-axis so that its velocity at anytime is t greater than or equal to 0 is given by v(t)=1-sin(2pi t)
a) find the acceleration a(t) of the particle at any time.
b) find all values of t, 0 <orequalto t <orequalto 2 for which the particle is at rest
c) find the position x(t) of the particle at any time if x(0)=0

anonymous · Answer

a) $a(t)= v^\prime(t)$
b) find the t when v(t)=0
c) $x(t)=\int\limits_{0}^{t}v(s)ds=\int\limits_{0}^{t}\left(1-\sin(2\pi s)\right) ds.$ Work out the integral.

anonymous · Answer

thanks