Yes, time dilation occurs when an object, including a spaceship, is accelerating. Time dilation is a phenomenon predicted by Einstein's theory of relativity, which states that time can appear to run slower for an object that is moving relative to an observer.
There are two types of time dilation: gravitational time dilation and velocity time dilation. Gravitational time dilation occurs due to the presence of a gravitational field, while velocity time dilation occurs when an object is moving at high speeds relative to an observer.
In the case of a spaceship accelerating, velocity time dilation would be the primary factor to consider. As the spaceship accelerates and approaches speeds close to the speed of light, time dilation effects become significant. From the perspective of an observer on Earth, time on the accelerating spaceship would appear to slow down relative to their own time.
This means that if two clocks were synchronized before the spaceship began accelerating, the clock on the spaceship would appear to run slower compared to the clock on Earth as the spaceship's velocity increases. As the spaceship approaches the speed of light, the time dilation effect would become more pronounced.
It's important to note that the magnitude of the time dilation effect would depend on the acceleration of the spaceship, its velocity, and the duration of the acceleration. The closer the spaceship's velocity is to the speed of light, the more pronounced the time dilation effect would be.