The cart comes to rest from 1.3 m/s in a matter of 0.30 s, so it undergoes an acceleration a of
a = (0 - 1.3 m/s) / (0.30 s)
a ≈ -4.33 m/s²
This acceleration is applied by a force of -65 N, i.e. a force of 65 N that opposes the cart's motion downhill. So the cart has a mass m such that
-65 N = m (-4.33 m/s²)
m = 15 kg