Determining the acceleration (\(a\)) of an object using the force and mass is a key concept in physics. The acceleration can be calculated using the rearranged formula:
\[ a = \dfrac{F}{m} \]
Where:
- \(a\) is the acceleration of the object (in meters per second squared, m/s²)
- \(F\) is the force acting on the object (in newtons, N)
- \(m\) is the mass of the object (in kilograms, kg)
Example 1: Calculating the Acceleration of a Motorcycle
Problem: A force of 600 N is applied to a motorcycle with a mass of 150 kg. What is the acceleration of the motorcycle?
Calculation:
Given:
- \(F = 600 \, \text{N}\)
- \(m = 150 \, \text{kg}\)
Using the formula:
\[ a = \dfrac{F}{m} = \dfrac{600}{150} = 4 \, \text{m/s}^2 \]
Answer: The acceleration of the motorcycle is 4 m/s².
Example 2: Calculating the Acceleration of a Cart
Problem: A force of 100 N is applied to a cart with a mass of 50 kg. What is the acceleration of the cart?
Calculation:
Given:
- \(F = 100 \, \text{N}\)
- \(m = 50 \, \text{kg}\)
Using the formula:
\[ a = \dfrac{F}{m} = \dfrac{100}{50} = 2 \, \text{m/s}^2 \]
Answer: The acceleration of the cart is 2 m/s².
Example 3: Calculating the Acceleration of a Skater
Problem: A force of 25 N is applied to a skater with a mass of 50 kg. What is the acceleration of the skater?
Calculation:
Given:
- \(F = 25 \, \text{N}\)
- \(m = 50 \, \text{kg}\)
Using the formula:
\[ a = \dfrac{F}{m} = \dfrac{25}{50} = 0.5 \, \text{m/s}^2 \]
Answer: The acceleration of the skater is 0.5 m/s².
