Question

3. The position of an object as a function of time in x-and y-coordinate system is given by n-( e k-cy where a 2m.b-5m's, and c- 10 m Find the (a) s- and (b) y components of instantaneous velocity at (e) speed of the objoct at r "3 s (d) total displacement of the object during 3

Answer 1

Given

$r(t)=(at^{2}+c)\widehat{i}+(bt-c)\widehat{j}$

where a=2 m/s² ,b=5 m/s ,c=10

V(t)=dr(t)/dt

$V(t)=(2at)\widehat{i}+b\widehat{j}$

a)

at t=3 s

V_x=2*2*3 =12 m/s²

b)

V_y=b=5 m/s

c)

V=sqrt[12²+5²]=13 m/s

d)

displacement

x=Vt =13*3 =39 m