Question

multiple choice question
the illustration represents the force on, and acceleration of, vehicles with different masses.
suppose that the force on the vehicles is the same. according to newtons second law of motion, how will the acceleration of the two vehicles compar
o there is not enough information to tell.
o the acceleration of the truck will be greater.
o their acceleration will be the same.
o the acceleration of the car will be greater.

Explanation:

Step1: Recall Newton's second law

Newton's second law is \(F = ma\) (where \(F\) is force, \(m\) is mass, and \(a\) is acceleration). We know for the car \(F_{car}=m_{car}a_{car}\), with \(m_{car} = 900\space kg\) and \(a_{car}=10\space m/s^{2}\), so \(F_{car}=900\times10 = 9000\space N\). Since the force on both vehicles is the same (\(F_{truck}=F_{car} = 9000\space N\)) and for the truck \(m_{truck}=1200\space kg\), we use \(a=\frac{F}{m}\) for the truck.

Step2: Calculate acceleration of the truck

For the truck, \(a_{truck}=\frac{F_{truck}}{m_{truck}}\). Substitute \(F_{truck} = 9000\space N\) and \(m_{truck}=1200\space kg\) into the formula: \(a_{truck}=\frac{9000}{1200}=7.5\space m/s^{2}\). Compare \(a_{car} = 10\space m/s^{2}\) and \(a_{truck}=7.5\space m/s^{2}\).

Answer:

The acceleration of the car will be greater.