Are seatbelts worn to protect passengers from speed or acceleration?

Answer 1

In a sense, yes. As a car accelerates, its passengers will also accelerate. As the passengers probably have less mass than the car, they accelerate differently to the car, which can cause their body to move quickly and suddenly (and may cause injury).

A seatbelt holds passengers in place in a car. As the car accelerates, passengers are restrained and cannot move greatly from their position in their seat, thus lowering the risk of injury.

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The above makes sense, but the seatbelts are more to protect from momentum, if you consider the first law of motion.

Momentum is p = mv (where p is momentum, m is mass and v is velocity). As a vehicle moves, according to the first law of motion, an object travelling at a certain state will continue to move in that state unless an external force acts upon it. Thusly, if you are riding in a vehicle and it is required to brake suddenly, the vehicle will stop, but your body - if it is not being impacted on by an external force such as a seatbelt - will continue to move forward with the same momentum which could possibly mean your body heading on its way through your windscreen.

(As a note, speed =/= velocity. Speed is a scalar quantity, whereas velocity is vector (has direction).)

When you combine the above response, and what was just written, you have your full answer.

Also, if you were wondering, seatbelts usually are both across the chest, and strapped across the hips because testing showed that one strap alone was not enough. Across the chest caused passengers to either slip out or caused decapitation, and across the waist/hips caused passengers' upper bodies to jerk forward (possible spinal damage, and damage to organs) in an accident. Thus, implementation of both allowed both bases to be covered effectively.