Straight line path.
Speed is the rate at which an object covers a particular distance. According to the question, the object was moving with constant speed, there is no change in the direction as well, This imply that the object is moving with constant velocity. No external forces applied on the object. Therefore the object is moving on a straight line path.
Straight linear path
If the universe were completely empty with just one object which is solid moving sphere through the space at a speed of 100km/s, it will move along on a straight path.
An object will continue on a straight path or at rest unless acted upon by an external force. This is the first law of newton.Since there is no other mass or body in the universe, it will move along in a straight line. Our planet and other bodies moves in parabolic path and elliptical orbits because they are attracted by the gravitational forces of other bodies. Any body with mass will attract other bodies and makes it move round it. The body with the less mass will orbit in the vicinity of the larger mass. But if we have just one body out there, there is no attraction from any other body, it will continue along it's straight path.