We consider longitudinal functional regression, where for each subject, we observe multiple 1D profiles (curves) over different time visits. We explore the idea of "projecting" the data onto 1D data driven directions and discuss significance tests based on "projections" in two general settings. First, we develop a test procedure to assess that the mean profile is time-invariant. Second, we extend the ideas to cross-over designs, to study if a treatment is significant in the presence of carryover effect. The tests have a non-standard null distribution that is easy to simulate from. Numerical studies confirm that the testing approaches have the correct size in finite samples and have a superior power relative to available competitors. The methods are illustrated on multiple sclerosis and wearable design applications.