A 1400 kg car accelerates uniformly from rest to 60 mph in 6 s. Find the net force needed to produce this motion.
The correct answer and explanation is:
To find the net force required to accelerate the car, we use Newton’s Second Law of motion: F=maF = ma
Where:
- FF is the net force (in newtons, N),
- mm is the mass (in kilograms, kg),
- aa is the acceleration (in meters per second squared, m/s²).
Step 1: Convert speed from mph to m/s
Final speed = 60 mph
To convert to meters per second: 60 mph=60×0.44704=26.8224 m/s60 \text{ mph} = 60 \times 0.44704 = 26.8224 \text{ m/s}
Step 2: Use acceleration formula
The car starts from rest, so initial velocity u=0u = 0.
Time t=6t = 6 s
Final velocity v=26.8224 m/sv = 26.8224 \text{ m/s}
Use the formula for acceleration: a=v−ut=26.8224−06=4.4704 m/s2a = \frac{v – u}{t} = \frac{26.8224 – 0}{6} = 4.4704 \text{ m/s}^2
Step 3: Use Newton’s Second Law
Mass m=1400m = 1400 kg
Acceleration a=4.4704 m/s2a = 4.4704 \text{ m/s}^2 F=ma=1400×4.4704=6258.56 NF = ma = 1400 \times 4.4704 = 6258.56 \text{ N}
✅ Final Answer:
6258.6 N(rounded to one decimal place)\boxed{6258.6 \text{ N}} \quad (\text{rounded to one decimal place})
Explanation (300 words)
To determine the net force required to accelerate a car, we use Newton’s Second Law, which states that the net force acting on an object equals the product of its mass and acceleration. The problem provides the car’s mass as 1400 kg and specifies that the car starts from rest and reaches 60 mph in 6 seconds. However, since SI units are used in physics calculations, we must first convert 60 mph to meters per second. Using the conversion factor 1 mph=0.44704 m/s1 \text{ mph} = 0.44704 \text{ m/s}, 60 mph becomes approximately 26.82 m/s.
Next, we calculate acceleration using the formula a=Δvta = \frac{\Delta v}{t}, where Δv\Delta v is the change in velocity and tt is the time. Since the car starts from rest, its initial velocity is 0, and the final velocity is 26.82 m/s. Dividing this by the 6-second interval gives an acceleration of approximately 4.47 m/s².
Now, applying Newton’s Second Law F=maF = ma, we multiply the car’s mass (1400 kg) by the calculated acceleration (4.47 m/s²), resulting in a net force of 6258.6 newtons. This net force is what’s required to uniformly accelerate the car from 0 to 60 mph in the given time. This value accounts only for the force to change velocity and doesn’t include resistance like friction or air drag, which would require even more force in real-world conditions.