Question

A small sports car collides head-on with a massive truck. Use propor- tional reasoning and Newton’s second law to predict which vehicle experiences the greater impact force, and which vehicle experiences the greater acceleration. Use equations to express your reasoning.

Answer 1

Both experience the same impact force according to Newton’s third law (equal but opposite). The smaller car experiences the greater acceleration because of its smaller mass, according to Newton’s second law (F=ma).

Answer 2

Both vehicles are influenced by the same force according to Newton's third law (same magnitude but opposite direction).

The smaller car experiences the greater acceleration because of its smaller mass, according to Newton's second law.

Step-by-step explanation:

Newton's third law

When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.

Hence, both vehicles are influenced by the same force.

`F_(AB)`: force exerted by the car

`F_(BA)`: force exerted by the truck

`F_(AB)=-F_(BA)`

Newton's second law

In an inertial frame of reference, the vector sum of the forces F on an object is equal to the mass m of that object multiplied by the acceleration a of the object: F = ma.

`F_(AB)= m*a_(car)`

`F_(BA)=M*a_(truck)`

`m*a_(car)=M*a_(truck)`

`(m)/(M) =(a_(truck))/(a_(car))`

As the sport car has smaller mass, it would have a bigger acceleration.