There are many reasons why a car makes a ticking sound when the accelerator is pushed. One of the most common reasons is the car is low on oil. If this is the problem, the sound will only occur after the car has warmed up. This is because oil is thicker when the car is first started, but thins down as the car warms up.
When there is not enough oil, the valves in the car make a ticking sound because they are not lubricated well enough. Another cause of a ticking sound is a worn timing belt. The timing belt keeps the crankshaft and the camshaft moving at the same speed. When the timing belt is worn, the timing can be off slightly, which often causes a ticking sound.
It is also possible that the wheel bearings or CV joints are causing the ticking sound if it only occurs when the car is first accelerating. Typically, if this is the cause of the sound, the noise will increase when the wheel is turned during acceleration. Another possible cause is a faulty transmission. To test this possibility, put the car in neutral and lightly press on the accelerator. If there is no ticking sound, have a mechanic look at the transmission.