A 975 kg car accelerates from rest to 26.7 m/s in a distance of 120 m. What is the magnitude of the average net force acting on the car
average velocity (v) is ... (0 + 26.7) / 2
time (t) is ... 120 / v
acceleration (a) is ... 26.7 / t
force is ... 975 * a
87
To find the magnitude of the average net force acting on the car, we can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration.
Given:
- Mass of the car (m) = 975 kg
- Initial velocity (u) = 0 m/s (since the car starts from rest)
- Final velocity (v) = 26.7 m/s
- Distance traveled (s) = 120 m
First, we can calculate the acceleration (a) using the formula:
v^2 = u^2 + 2as
Rearranging the formula, we get:
a = (v^2 - u^2) / (2s)
Substituting the given values, we have:
a = (26.7^2 - 0^2) / (2 * 120)
a = 357.57 m^2/s^2 / 240
a ≈ 1.49 m/s^2
Now we can calculate the net force (F_net) using Newton's second law:
F_net = m * a
Substituting the given value for the mass and the calculated acceleration, we have:
F_net = 975 kg * 1.49 m/s^2
F_net ≈ 1450.55 N
Therefore, the magnitude of the average net force acting on the car is approximately 1450.55 N.
To find the magnitude of the average net force acting on the car, we can use Newton's second law of motion, which states that the force acting on an object is equal to the product of its mass and acceleration.
Step 1: Find the acceleration of the car.
Given that the car starts from rest and reaches a velocity of 26.7 m/s, we can use the formula for acceleration (a = Δv / Δt) where Δv is the change in velocity and Δt is the time taken.
Since the car starts from rest, the initial velocity (u) is 0 m/s, and the final velocity (v) is 26.7 m/s.
Using the formula:
a = (v - u) / t
a = (26.7 - 0) / t
However, we are not given the time taken (Δt) to accelerate. Instead, we are given the distance traveled (120 m). So, we need to find the time taken using the following equation:
s = ut + (1/2)at^2
where s is the distance, u is the initial velocity, t is the time taken, and a is the acceleration.
Since the car starts from rest (u = 0), the equation simplifies to:
s = (1/2)at^2
120 = (1/2)a × t^2
Simplifying further, we get:
240 = at^2
Now, we need to solve for time (t):
t^2 = 240 / a
t = sqrt(240 / a)
Step 2: Calculate the acceleration and substitute the time value back in the acceleration equation.
We can substitute the value of time (t) back into the acceleration equation to calculate the acceleration (a):
a = (26.7 - 0) / t
Now that we have calculated the acceleration, we can move on to find the magnitude of the average net force acting on the car.
Step 3: Calculate the magnitude of the average net force.
The magnitude of the average net force can be found using the formula:
F = m × a
where F is the force, m is the mass, and a is the acceleration.
Given that the mass of the car (m) is 975 kg and the acceleration (a) is calculated in the previous step, we can substitute these values into the equation:
F = 975 × a
By plugging in the calculated value of acceleration, you will get the magnitude of the average net force acting on the car.