Answer:
Explanation:
angular position u = 4[tex]t^{3/2}[/tex]
radial position r = .1t³
s = length of arc = ru
= 4[tex]t^{3/2}[/tex] x .1t³
= .4 [tex]t^{9/2}[/tex]
ds/dt = .4 x 9/2 x [tex]t^{7/2 }[/tex]
tangential velocity
Vt = 1.8 x [tex]1.5^{7/2 }[/tex]
= 7.44 m /s
tangential acceleration At =1.8x 7/2 x [tex]1.5^{5/2}[/tex]
= 17.36 m /s²
radial velocity Vr = dr/dt
= .3t²
= .3 x 1.5 ²
= .675 m/s
radial acceleration Ar = dVr / dt
= .6t = .6 x 1.5
= .9 m /s²
total velocity = √( Vt² + .Vr²) = √( 7.44² + .675²) = 7.47 m /s
total acceleration = √ (At² + Ar ²) = √ 17.36² + .9² = 17.38 m /s²
