Question

How would the measurement of acceleration (magnitude) be affected if instead of starting from rest, the cart was given an intial velocity a) down the incline? b) up the incline?

Answer 1

In both the cases, the acceleration will remain same.

The acceleration doesn't get affected by initial velocity. Consider an example.

Case - 1 : You drop a ball from top of your roof without giving it any initial velocity.

Case - 2 : You throw down the ball from your roof which means you gave it some initial velocity.

In both the cases, the acceleration acting on the ball would remain same. And that would be acceleration due to gravity 'g'.

Similarly, on an incline it doesn't matter if you start from rest, give it some initial velocity up the incline or down the incline; the magnitude of the acceleration would remain same.

Here is the schematic free body diagram of the situation -