Mach 1.5 at STP is roughly 500 m/s. That's not particularly exciting... consider that a Barrett M82 has a muzzle velocity of nearly 900 m/s, and a General Dynamics KEW-A1 (a real-world APFSDS antitank round) manages 1740 m/s. Your arrow is so slow that the various armor penetration calculators and algorithms I could find online refused to accept it... anything lower than rifle-like velocities of 8-900 m/s was considered too low for the equation to reasonably work. This strongly suggests to me that your projectile design is wrong... "long rod penetrators" work at significantly higher velocities than your design, so you probably don't get nearly as much benefit from that style of projectile as you might have thought.
Your projectile is 1 m long and 9 mm in diameter, giving an L/D ratio of ~111:1. That's a significantly more slender shape than typical antitank rounds... the largest L/D ratio I kind find in 120x570mm NATO tank rounds is 37:1. Given that manufacturers of antitank rounds are well aware that armor penetration is a function of the length of the penetrator, you can assume that they worked out the longest aspect they could get away with before some other effects started impairing ammunition performance... maybe at the point of shooting, maybe in-flight, maybe at the point of impact, I'm not certain. In whichever case, your "arrow" is almost certainly too long, and even if it were travelling at significantly higher velocities your skinny aspect ratio will probably impair its ability to use its full length for armor penetration.
Your projectile masses approximately 1kg. To accelerate that projectile to that speed over its own length requires an average acceleration of 125000 m/s2, which isn't completely unreasonable by gun standards. If pressure in the barrel were constant, you could pack your arrow in a 20 mm diameter sabot and use a conventional propellant to get a chamber pressure of ~400 MPa which is similar to that in the Barret M82. Problem is, pressure in the barrel isn't constant, as it rises quickly to a peak and drops off, and it is sufficiently complex to compute I'm not going to try. If you used a chemical propellant for your gun, you might need either a much wider barrel or a much tougher one to withstand the shot (and that means weight). Note that conventional weapons throwing a ~1kg round include 40 mm autocannon, that have quite a chunky barrel that tends to be 50-70 calibers long (eg. 2-2.8 m), which eases performance requirements slightly (and probably helps accuracy a lot). Admittedly they have a much higher muzzle velocity, because 500 m/s is too slow to be useful to anyone, really.
If you used a coilgun to throw your round, then Luke Campbell's approximation suggests you'd need a field strength of ~80 T, which implies some serious high-temperature superconductors on top of all your other material requirements.
You should consider that your design is problematic on multiple fronts, and you're attempting to overcomplicate something that has already been solved using much simpler and more practical technology.
Consider that things like the M18 recoilless rifle or even the classic bazooka offered economical and readily human portable antitank weaponry with armor penetration exceeding that of antitank rifles (which in turn were often more powerful than the .50 rounds you mention, eg. Lahti L-39, a 20mm rifle) over 80 years ago. Even the ubiquitous RPG-7 is 65 years old, is straightfoward and cheap to manufacture, robust and easy to use and offers up to 750 mm penetration (though 300 mm seems more likely) of RHA... vastly more than your arrow could be capable of. Lighter futuristic equivalents could have more compact projectiles offering higher velocities and longer ranges and armor penetration suitable for lighter targets, and they could use other projectile types (fragmentation, thermobaric, whatever) for other targets making them much more versatile.
(you could even look at modern high-velocity 40 mm grenades, which can penetrate ~50-80 mm of RHA using a shaped charge warhead, and are smaller, lighter and more versatile than your arrows, as another option)