A particle in the plane has velocity v(t)=⟨2t,t2⟩ for all real t. Its acceleration is a(t)=⟨2,2t⟩. For t>0, which statement best describes the behavior of the particle’s speed?
a) The speed decreases for all t>0 because v(t)⋅a(t)<0.
b) The speed increases on (0,1) and decreases for t>1 because v(t)⋅a(t) changes sign at t=1.
c) The speed increases for all t>0 because v(t)⋅a(t)>0.
d) The speed remains constant for all t>0 because ∣v(t)∣ is independent of t.