A car of mass 1200 kg starts from rest, accelerates uniformly to a speed of 4.0 m/s in 2.0 s and continues moving at this constant speed in a
horizontal straight line for an additional 10 s. The brakes are then applied and the car is brought to rest in 4.0 s. A constant resistance
force of 500 N is acting on the car during its entire motion.
Calculate the force accelerating the car in the first 2.0 s of the motion.
phase 1:
av speed = 4/2 = 2 m/s
x = 0 + 2 t = 4 meters
phase 2
v = 4 m/s
x = 4 + 10*4 = 4 + 40
phase 3
Vi = 4 m/s
Xi = 44
average v = 2
x = 44 + 2*4 = 52 meters total
work done by resistance during phase 1 = 500 N * 4 meters =2000 Joules
kinetic energy gained during phase 1
=(1/2)1200 (4^2) = 9600 Joules
so total energy input during phase 1
= 11,600 Joules
That is force * distance
and distance = 4 meters
To calculate the force accelerating the car in the first 2.0 seconds, we can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration (F = ma).
Given:
Mass of the car (m) = 1200 kg
Initial velocity (u) = 0 m/s
Final velocity (v) = 4.0 m/s
Time taken (t) = 2.0 s
Resistance force (Fr) = 500 N
First, let's calculate the acceleration of the car during the first 2.0 seconds using the formula:
a = (v - u) / t
a = (4.0 m/s - 0 m/s) / 2.0 s
a = 4.0 m/s / 2.0 s
a = 2.0 m/s^2
Now, we can calculate the force accelerating the car:
F = m * a
F = 1200 kg * 2.0 m/s^2
F = 2400 N
Therefore, the force accelerating the car in the first 2.0 seconds of motion is 2400 Newtons.
To calculate the force accelerating the car in the first 2.0 s of motion, we first need to find the net force acting on the car during this period. We can do this by considering the forces acting on the car.
The net force acting on an object is given by Newton's second law of motion, which states that the net force is equal to the mass of the object multiplied by its acceleration:
Net force = mass × acceleration
During the first 2.0 s, the car accelerates uniformly from rest to a speed of 4.0 m/s. The acceleration can be calculated using the equation of motion:
acceleration = (final velocity - initial velocity) / time
Substituting the given values, we have:
acceleration = (4.0 m/s - 0 m/s) / 2.0 s
acceleration = 4.0 m/s / 2.0 s
acceleration = 2.0 m/s²
Now we can calculate the net force:
Net force = mass × acceleration
Net force = 1200 kg × 2.0 m/s²
Net force = 2400 N
However, we need to take into account the constant resistance force of 500 N acting in the opposite direction. Since resistance force opposes the motion, we need to subtract it from the net force:
Force accelerating the car = Net force - Resistance force
Force accelerating the car = 2400 N - 500 N
Force accelerating the car = 1900 N
Therefore, the force accelerating the car in the first 2.0 s of motion is 1900 N.