Select the correct answer.
A force of 15 newtons is applied to both Object A with a mass of 25 kilograms and Object B with a mass of 50 kilograms. What is true about the acceleration of Object A and Object B?

A. Acceleration of Object A is four times that of the acceleration of Object B.
B. Acceleration of Object A is the same as the acceleration of Object B.
C. Acceleration of Object A is half the acceleration of Object B.
D. Acceleration of Object A is twice that of the acceleration of Object B

Apply Newton's second law of motion: F = ma .
Calculate the acceleration of Object A: a A ​ = 25 15 ​ = 0.6 m/s 2 .
Calculate the acceleration of Object B: a B ​ = 50 15 ​ = 0.3 m/s 2 .
Compare the accelerations: The acceleration of Object A is twice that of Object B. Acceleration of Object A is twice that of the acceleration of Object B ​

Explanation

Problem Analysis We are given that a force of 15 N is applied to two objects: Object A with a mass of 25 kg and Object B with a mass of 50 kg. We need to determine the relationship between the accelerations of the two objects.

Applying Newton's Second Law We will use Newton's second law of motion, which states that Force = mass × acceleration, or F = ma . We can rearrange this formula to solve for acceleration: a = m F ​ .

Calculating Acceleration of Object A For Object A, the force is 15 N and the mass is 25 kg. Therefore, the acceleration of Object A is: a A ​ = 25 kg 15 N ​ = 0.6 m/s 2

Calculating Acceleration of Object B For Object B, the force is 15 N and the mass is 50 kg. Therefore, the acceleration of Object B is: a B ​ = 50 kg 15 N ​ = 0.3 m/s 2

Comparing Accelerations Now we compare the accelerations of Object A and Object B. We can find the ratio of their accelerations: a B ​ a A ​ ​ = 0.3 m/s 2 0.6 m/s 2 ​ = 2
This means that the acceleration of Object A is twice the acceleration of Object B.

Conclusion Therefore, the correct answer is that the acceleration of Object A is twice that of the acceleration of Object B.


Examples
Newton's second law is fundamental in understanding how forces affect the motion of objects. For example, consider a car of mass 1000 kg accelerating at 2 m/s². The force required to produce this acceleration is F = ma = 1000 kg × 2 m/s 2 = 2000 N . This principle is used in designing vehicles, calculating braking distances, and understanding the impact of collisions. Understanding the relationship between force, mass, and acceleration is crucial in many real-world applications, from engineering to sports.

Answered by GinnyAnswer | 2025-07-06