Question

math-based practice

1. a semi-truck collides with a car with a force of 5000n. the semi-truck has a mass of 2000kg and the car has a mass of 500kg.

→what was the acceleration of the truck when it hit the car?
→what force did the car exert on the semi-truck at impact?
→how much did the car accelerate when it was hit?
→if the action statement is the semi-truck exerts a force on the car, what is the reaction statement?

Explanation:

Step1: Calculate the acceleration of the truck

According to Newton's second law \(F = ma\), so \(a=\frac{F}{m}\). For the truck, \(F = 5000N\) and \(m = 2000kg\).
\(a_{truck}=\frac{5000}{2000}= 2.5m/s^{2}\)

Step2: Determine the force the car exerted on the truck

By Newton's third law, the force of action and reaction are equal in magnitude and opposite in direction. So the force the car exerted on the truck is \(5000N\)

Step3: Calculate the acceleration of the car

Using \(a=\frac{F}{m}\) again. For the car, \(F = 5000N\) and \(m = 500kg\)
\(a_{car}=\frac{5000}{500}=10m/s^{2}\)

Step4: State the reaction statement

Based on Newton's third law, if the action is “The semi - truck exerts a force on the car”, the reaction is “The car exerts an equal and opposite force on the semi - truck”

Answer:

• The acceleration of the truck: \(2.5m/s^{2}\)
• The force the car exerted on the truck: \(5000N\)
• The acceleration of the car: \(10m/s^{2}\)
• The reaction statement: “The car exerts an equal and opposite force on the semi - truck”