To calculate the force needed to accelerate a vehicle, we can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration (F = ma). In this case, the acceleration is given as 3 m/s² and the mass of the vehicle is 100 kg. Let's break down the calculation step by step:

1. Identify the given values:
- Mass of the vehicle (m) = 100 kg
- Acceleration (a) = 3 m/s²

2. Determine the force required:
- Using Newton's second law of motion (F = ma), substitute the known values into the equation:
F = 100 kg × 3 m/s²
- Multiply the mass (100 kg) by the acceleration (3 m/s²):
F = 300 kg⋅m/s²

3. Simplify the units:
- The unit of force is the newton (N), which is equivalent to kg⋅m/s².
- So, the force required to accelerate the vehicle to 3 m/s² is:
F = 300 N

Therefore, a force of 300 newtons (N) will be needed to accelerate the vehicle to 3 m/s².

Summary:
- Mass of the vehicle (m) = 100 kg
- Acceleration (a) = 3 m/s²
- Using Newton's second law of motion (F = ma), we can find the force required.
- Substitute the known values: F = 100 kg × 3 m/s²
- Simplify the units: F = 300 N
- Therefore, a force of 300 newtons (N) will be needed to accelerate the vehicle to 3 m/s².

Force=ma
Given: m=100kg, a=3m/^2
F=100kg×3m/s^2
F=300N (Ans).