In our Solar System, the planets formed by collisional growth from smaller bodies. Planetesimals collided to form Moon-to-Mars-sized protoplanets in the inner Solar System in 0.1-1 Myr, and these collided more energetically to form planets. Insights into the timing and nature of collisions during planetary accretion can be gained from meteorite studies. In particular, iron meteorites offer the best constraints on early stages of planetary accretion because most are remnants of the oldest bodies, which accreted and melted in <1.5 Myr, forming silicate mantles and iron-nickel metallic cores. Cooling rates for various groups of iron meteorites suggest that if the irons cooled isothermally in the cores of differentiated bodies, as conventionally assumed, these bodies were 5-200 km in diameter. This picture is incompatible, however, with the diverse cooling rates observed within certain groups, most notably the IVA group, but the large uncertainties associated with the measurements do not preclude it. Here we report cooling rates for group IVA iron meteorites that range from 100 to 6,000 K Myr(-1), increasing with decreasing bulk Ni. Improvements in the cooling rate model, smaller error bars, and new data from an independent cooling rate indicator show that the conventional interpretation is no longer viable. Our results require that the IVA meteorites cooled in a 300-km-diameter metallic body that lacked an insulating mantle. This body probably formed approximately 4,500 Myr ago in a 'hit-and-run' collision between Moon-to-Mars-sized protoplanets. This demonstrates that protoplanets of approximately 10(3) km size accreted within the first 1.5 Myr, as proposed by theory, and that fragments of these bodies survived as asteroids.