What average force is required to stop an 1600 -kg car in 8.0 s if the car is traveling at 80 km/h?
To find the average force required to stop the car, we need to follow these steps:
Step 1: Convert the car's speed from km/h to m/s.
Step 2: Calculate the change in velocity of the car.
Step 3: Calculate the time it takes to stop the car.
Step 4: Use Newton's second law to find the average force.
Let's go through each of these steps in detail.
Step 1: Convert the car's speed from km/h to m/s.
To convert km/h to m/s, we need to divide the speed by 3.6 since 1 km/h is equal to 1/3.6 m/s.
Speed in m/s = 80 km/h / 3.6 = 22.222 m/s (rounded to 3 decimal places)
Step 2: Calculate the change in velocity of the car.
The car is initially traveling at 80 km/h (22.222 m/s), and it needs to come to a complete stop. Therefore, the change in velocity (∆v) is equal to the initial velocity (v) since the final velocity is 0.
∆v = 22.222 m/s
Step 3: Calculate the time it takes to stop the car.
The time it takes to stop the car is given as 8.0 s.
Time (t) = 8.0 s
Step 4: Use Newton's second law to find the average force.
Newton's second law states that the force (F) is equal to the mass (m) multiplied by the acceleration (a).
F = m * a
Since the car needs to come to a complete stop, the acceleration (a) can be calculated using the equation:
a = ∆v / t
Plugging in the values:
a = 22.222 m/s / 8.0 s = 2.778 m/s² (rounded to 3 decimal places)
Now, we have the acceleration, and we can calculate the average force:
F = 1600 kg * 2.778 m/s² = 4444 N (rounded to the nearest whole number)
Therefore, the average force required to stop the 1600 kg car traveling at 80 km/h in 8.0 s is approximately 4444 N.
To calculate the average force required to stop the car, we need to use 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.
1. First, we need to determine the initial velocity of the car. The initial velocity is given as 80 km/h. However, it is important to convert this to m/s because the formula requires the units to be consistent. We know that 1 km/h is equal to 0.2778 m/s. So, the initial velocity of the car is:
Initial velocity = 80 km/h × 0.2778 m/s = 22.222 m/s
2. Next, we need to determine the final velocity of the car. Since the car comes to a stop, the final velocity is 0 m/s.
3. Now, we can calculate the acceleration of the car. In order to find the acceleration, we can use the equation:
v^2 = u^2 + 2as,
where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance covered.
In this case, v = 0 m/s, u = 22.222 m/s, and s is unknown. We are given the time it takes to stop, which is 8.0 s. Since the car starts with a positive velocity and comes to a stop, we can use the equation:
s = ut + (1/2)at^2,
where s is the distance covered, u is the initial velocity, t is the time, and a is the acceleration.
Plugging in the values we know, we have:
s = (22.222 m/s)(8.0 s) + (1/2)a(8.0 s)^2.
Since we are solving for acceleration, we can rearrange the equation to:
a = 2(s - ut) / t^2.
Plugging in the values we know, we get:
a = 2(0 - (22.222 m/s)(8.0 s)) / (8.0 s)^2 = -6.9444 m/s^2
4. Finally, we can calculate the average force required to stop the car by using Newton's second law:
Force = mass × acceleration,
where mass is given as 1600 kg and acceleration is -6.9444 m/s^2 (negative because it is decelerating).
Therefore:
Force = 1600 kg × -6.9444 m/s^2 = -11,111 N (rounded to the nearest whole number).
The average force required to stop the car is approximately 11,111 N in the opposite direction of its motion.