A white Rover 416 pulling out of Mayfield Close collided with a blue Volvo FM lorry on the southbound carriageway of the A24 close to Durrington cemetery at 4pm on Tuesday (April 15).
The road had to be closed southbound while the scene was made safe and officers began their investigation.
The 89-year-old man from Worthing who was driving the Rover suffered a fractured breastbone.
His 85-year-old passenger, also from Worthing, suffered a fractured arm and a fractured leg.
The 43-year-old lorry driver, from Worthing, was not injured.
A police spokesman said: “The A24 would have been very busy when the collision happened so we are hoping that there could be witnesses who saw the crash.
“If you were driving or walking in the area, or saw what happened from your home, please contact us.”
Anyone who saw the collision should call 101 quoting serial 965 of 15/4 or email [email protected]