C172 Student Pilot reported the aircraft lacked the proper airspeed during takeoff and the Flight Instructor aborted takeoff.

Narrative

I was student preparing to fly with my CFI to complete my fourth flying lesson. CFI took controls at run-up for takeoff - I handed over controls after taxi to run-up. After getting clearance; CFI proceeded to runway but passed runway by approximately 10 - 20 ft. However; CFI proceeded to take off on the roll from run-up. Full throttle with rich mixture; all instruments showed no issue as airspeed came alive. At around 45 mph; airspeed stopped climbing and the engine felt like it couldn't push any further; despite no issues indicated by instruments. CFI tried to take off and the plane came off the ground slightly; but as CFI realized we did not have enough airspeed; it was decided to abort. CFI stopped the plane before the end of the runway with my assistance pressing on the brakes. CFI maintained all controls until we returned to FBO.Before takeoff; run-up checklist was rushed due to traffic; using a different/shorter runway; and potentially marginal VFR conditions approaching. These are the possible reasons why CFI took controls during run-up prior to takeoff as I believe I was taking too much time as a student trying to work through my checklist.