Question

17 in a collision between a truck and a motorcycle which vehicle experiences the greater acceleration? a truck b motorcycle c both experience the same acceleration

Explanation:

Step1: Apply Newton's third law

According to Newton's third law, in a collision, the force \(F\) exerted by the truck on the motorcycle is equal in magnitude and opposite in direction to the force exerted by the motorcycle on the truck (\(F_{truck - motorcycle}=F_{motorcycle - truck}\)).

Step2: Use Newton's second law \(F = ma\) (where \(F\) is force, \(m\) is mass, and \(a\) is acceleration, so \(a=\frac{F}{m}\))

Let \(m_{truck}\) be the mass of the truck and \(m_{motorcycle}\) be the mass of the motorcycle. We know that \(m_{truck}>m_{motorcycle}\). Since \(F_{truck - motorcycle}=F_{motorcycle - truck}\), and \(a=\frac{F}{m}\), for the truck \(a_{truck}=\frac{F}{m_{truck}}\) and for the motorcycle \(a_{motorcycle}=\frac{F}{m_{motorcycle}}\).

Step3: Compare accelerations

Because \(m_{truck}>m_{motorcycle}\) and \(F\) (the magnitude of the force) is the same for both (from Newton's third law), when we divide the same force \(F\) by a smaller mass (\(m_{motorcycle}\)), the acceleration \(a_{motorcycle}\) will be larger. Mathematically, if \(F\) is constant and \(m_{1}>m_{2}\), then \(\frac{F}{m_{1}}<\frac{F}{m_{2}}\).

Answer:

B. motorcycle