The production of top quark-antiquark pair events in $p\bar{p}$ collisions at $\sqrt{s}=1.96$ TeV is studied as a function of the transverse momentum and absolute value of the rapidity of the top quarks as well as of the invariant mass of the $t\bar{t}$ pair. We select events containing an isolated lepton, a large imbalance in transverse momentum, and four or more jets with at least one jet identified to originate from a $b$ quark. The data sample corresponds to 9.7 fb$^{-1}$ of integrated luminosity recorded with the D0 detector during Run II of the Fermilab Tevatron Collider. Observed differential cross sections are consistent with standard model predictions.