Question

the truck shown below has eight times the mass of the car. how can the truck accelerate at the same rate as the car (0 - 60 mph in 8 second)? the net force on the truck needs to be eight times larger. the net force on the truck needs to be eight times smaller. the net force on the truck needs to be four times smaller. the net force on the truck needs to be four times larger.

Explanation:

Step1: Recall Newton's second law

Newton's second law is \(F = ma\), where \(F\) is the net force, \(m\) is the mass, and \(a\) is the acceleration.

Step2: Analyze the relationship between force, mass and acceleration for car and truck

Let the mass of the car be \(m_{car}\), the mass of the truck be \(m_{truck}=8m_{car}\), the acceleration of the car be \(a_{car}\) and the acceleration of the truck be \(a_{truck}\). Given \(a_{truck}=a_{car}\).
For the car: \(F_{car}=m_{car}a_{car}\). For the truck: \(F_{truck}=m_{truck}a_{truck}\). Substitute \(m_{truck}=8m_{car}\) and \(a_{truck}=a_{car}\) into the truck's force formula, we get \(F_{truck}=8m_{car}a_{car}\). Since \(F_{car}=m_{car}a_{car}\), then \(F_{truck} = 8F_{car}\).

Answer:

The net force on the truck needs to be eight times larger.