Linear interpolation: reach moving destination regardless its speed

I’m implementing a camera for a game and I’m using the LERP formula for smooth chasing. However, if the target moves fast enough, the camera can never reach it unless the t ((1 – t) * v0 + t * v1) value is high enough, but that is exactly the problem: some targets might still move faster than the current t value.

This might lead to 2 problems:

1. The camera will never reach the object if it’s super fast
2. The camera will very slowly reach the object, depending on its
   current speed

How do I scale up my t when the delta distance (abs(v1 - v0)) gets lower, so that the camera will starts at a slow chasing rate and increases as it gets closer (therefore no targets could run away)?

f = some constant smoothing factor between 0 and 1
t = min(t + f, 1)
v0 = (1 - t) * v0 + t * v1 // lerp