Calculating the Force Required to Accelerate a Vehicle

To calculate the force required to accelerate a vehicle, we need to apply Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.

Given:
Mass of the vehicle (m) = 100 kg
Acceleration (a) = 3 m/s²

Using the formula: Force (F) = mass (m) × acceleration (a)

1. Calculate the force:
F = m × a
F = 100 kg × 3 m/s²
F = 300 N

Therefore, the force required to accelerate the vehicle to 3 m/s² is 300 Newtons.

Explanation:
To understand the concept, it is essential to know the fundamental principles involved:

1. Newton's Second Law of Motion:
Newton's second law of motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Mathematically, it can be represented as:
F = m × a

2. Mass (m):
Mass is the measure of the amount of matter an object contains. In this case, the mass of the vehicle is given as 100 kg.

3. Acceleration (a):
Acceleration is the rate at which an object changes its velocity. Here, the vehicle needs to be accelerated to a velocity of 3 m/s².

4. Calculating the Force:
By substituting the given values into the formula F = m × a, we can calculate the force required. In this case, the force required to accelerate the vehicle to 3 m/s² is 300 Newtons.

Therefore, in order to achieve an acceleration of 3 m/s², a force of 300 Newtons needs to be applied to the vehicle.