Final answer:
To accelerate a 1200 kg car to a speed of 80 km/h in 8 seconds, the force required is approximately 3000 N, calculated using the unit conversion for speed and Newton's second law of motion.
Step-by-step explanation:
To find the force required to accelerate a 1200 kg car from rest to a speed of 80 km/h east in 8.0 seconds, we will first convert the velocity to meters per second (SI units), then calculate acceleration, and apply Newton's second law of motion.
First, convert the speed from km/h to m/s:
80 km/h = ≈ 22.22 m/s (since 1 km/h is approximately 0.2778 m/s).
Next, calculate the car's acceleration (a) using the formula:
a = ∆v / ∆t
where ∆v is the change in velocity (22.22 m/s) and ∆t is the change in time (8.0 s).
Therefore, a = 22.22 m/s / 8 s = 2.78 m/s².
Now, apply Newton's second law:
F = ma
where m is the mass of the car (1200 kg) and a is the acceleration (2.78 m/s²).
So, F = 1200 kg × 2.78 m/s² = 3336 N, which rounds to 3000 N considering the options given in the question.