how large a force is required to accelerate a 1300kg car from rest to a speed 20m/s in a distance of 80m?
force * distance = kinetic energy
f * 80 m = 1/2 * 1300 kg * (20 m/s)^2
answer is in Newtons
how large a force required to accelerate 1300kg car from rest to speed 20m/s in a distance of 80m
To determine the force required to accelerate a car, we can use Newton's second law of motion, which states that
force = mass × acceleration.
First, we need to calculate the acceleration of the car. We can use the following equation:
acceleration = (final velocity - initial velocity) / time,
where the initial velocity is 0 since the car is at rest, the final velocity is 20 m/s, and the time is calculated using the formula distance = initial velocity × time + 0.5 × acceleration × time^2.
Given that the distance is 80 m, let's calculate the time it takes for the car to travel this distance:
distance = initial velocity × time + 0.5 × acceleration × time^2.
Since the initial velocity is 0, the equation simplifies to:
80 = 0.5 × acceleration × time^2.
Next, we'll solve for time:
Time = sqrt(2 × distance / acceleration).
Now we can calculate the acceleration:
acceleration = (final velocity - initial velocity) / time.
Plugging in the values, we have:
acceleration = (20 - 0) / time.
Finally, we can calculate the force required using Newton's second law:
force = mass × acceleration.
Given that the mass of the car is 1300 kg, let's substitute the values into the equation to find the force required.
To calculate the force required to accelerate the car, we can use Newton's second law of motion, which states that the force (F) acting on an object is equal to its mass (m) multiplied by its acceleration (a). In this case, we need to find the acceleration first.
The acceleration can be determined using the formulas of kinematics. We have the initial velocity (u) as 0 m/s (since the car is at rest), the final velocity (v) as 20 m/s, and the distance traveled (s) as 80 m. We can use the equation:
v^2 = u^2 + 2as
Substituting the given values:
20^2 = 0^2 + 2a(80)
400 = 160a
Dividing both sides by 160:
a = 400/160 = 2.5 m/s^2
Now that we have the acceleration, we can calculate the force required to accelerate the car:
F = m * a
F = 1300 kg * 2.5 m/s^2
F = 3250 Newtons
Therefore, a force of 3250 Newtons is required to accelerate the 1300 kg car from rest to a speed of 20 m/s in a distance of 80 m.