diff --git a/src/roboticstoolbox/tools/trajectory.py b/src/roboticstoolbox/tools/trajectory.py
index 87f3d85a4..95386c8ab 100644
--- a/src/roboticstoolbox/tools/trajectory.py
+++ b/src/roboticstoolbox/tools/trajectory.py
@@ -724,7 +724,7 @@ def __init__(self, q0: float, qf: float, T: float, V: float | None = None) -> No
             self._a = 0.0
         else:
             self.tb = (q0 - qf + vel * T) / vel
-            self._a = vel / self.tb
+            self._a = 0.0 if self.tb == 0 else vel / self.tb
 
         self.V = vel
         self._q0 = q0
@@ -753,6 +753,10 @@ def __call__(self, t: Any) -> Any:
         for k, tk in enumerate(times.flat):
             if tk < 0:
                 pk, pdk, pddk = q0, 0.0, 0.0
+            elif tb == 0 and tk <= T:
+                pk = q0 + V * tk
+                pdk = V
+                pddk = 0.0
             elif tk <= tb:
                 # initial blend
                 pk = q0 + a / 2 * tk**2
diff --git a/tests/test_trajectory.py b/tests/test_trajectory.py
index f067dc563..07c0ea6c5 100644
--- a/tests/test_trajectory.py
+++ b/tests/test_trajectory.py
@@ -87,6 +87,16 @@ def test_trapezoidal_time_origin(self) -> None:
                             getattr(actual, field), getattr(expected, field), atol=1e-12
                         )
 
+    def test_trapezoidal_zero_blend_velocity_boundary(self) -> None:
+        for q0, qf in ((0.0, 1.0), (1.0, 0.0)):
+            with self.subTest(q0=q0, qf=qf):
+                trajectory = tr.trapezoidal(q0, qf, np.array([0.0, 0.5, 1.0]), V=1.0)
+
+                self.assertEqual(trajectory.tblend, 0.0)
+                nt.assert_allclose(trajectory.q, [q0, 0.5, qf])
+                nt.assert_allclose(trajectory.qd, np.full(3, qf - q0))
+                nt.assert_allclose(trajectory.qdd, np.zeros(3))
+
     def test_mtraj_time_origin(self) -> None:
         elapsed = np.linspace(0, 2, 9)
         for generator in (tr.quintic, tr.trapezoidal):