From the velocity of an object find the displacement from a given starting point.?

The velocity is V = 2 cos(t) + 3 sin(t)


Find the displacement from the starting point at:


1) 蟺/2


2) 蟺


3) 2蟺





please help (with workings) thank you very much!From the velocity of an object find the displacement from a given starting point.?
Let s(t) be the displacement from starting point. Then,


s(t) = Integral(0 to t)[Vdt] = Integral(0 to t)[{2 cos(t) + 3 sin(t)}dt] or


= [2sin (t)],0 to t - 3cos(t)], o to t or


= 2sin (t) - [1-3 cos(t)] = 2 sin(t) + 3 cos(t) -1. So answers are:


1) 2+0-1 = 1; 2) 0-3-1 = -4; 3) 0+3-1 = 2From the velocity of an object find the displacement from a given starting point.?
v=2cos(t)+3sin(t)


we know s=integral of vdt from 0 to t


i think i can skip the integration part


when we integrate we get s=2sin(t)-3cos(t)





since it is displacement, a vector quantity we can use the resulting function for displacement for finding displacement





if it had been distance it would have to be i think modulus of v integrated w.r.t to time





just putting in values


1)2*1-3*0=2


2)2*0-3*(-1)=3


3)2*0-3*1= -3 means a displacement in opp. direction when considered wrt to earlier 2 displacements