A racing car of mass 850 kg accelerates from 20 km/h to 160 km/h over a distance of 300 metres. Frictional forces and wind resistance can be assumed to be 800N.
Determine the following:
(i)The average acceleration
(ii)The time taken to accelerate from 20 km/h to 160 km/h
(iii)The tractive force produced by the car to provide this acceleration
(iv)The car finally reaches a speed of 250km/h. Friction and wind resistance are 1800 N at this speed. What power output is required to maintain this speed?
i. vf^2=vi^2+2ad change velocities to m/s, then solve for a.
ii. vf=vi+at solve for t
iii. Force=a/mass
iv. power=(force*velocity)=(1800*V) where V is in m/s
To answer these questions, we can use the equations of motion and the concepts of Newton's laws of motion.
(i) The average acceleration can be determined using the equation:
average acceleration = (final velocity - initial velocity) / time
Here, the initial velocity is 20 km/h and the final velocity is 160 km/h. We need to convert these velocities to m/s. Remember that 1 km/h = 1000 m/3600 s. So, the initial velocity is 20 km/h * (1000 m/3600 s) = 5.56 m/s and the final velocity is 160 km/h * (1000 m/3600 s) = 44.44 m/s.
The time is not given directly, but we can find it using the equation of motion:
final velocity^2 = initial velocity^2 + 2 * acceleration * distance
Here, the distance is given as 300 meters, and the initial and final velocities are as calculated above. Rearranging the equation, we have:
acceleration = (final velocity^2 - initial velocity^2) / (2 * distance)
Substituting the values, we get:
acceleration = (44.44^2 - 5.56^2) / (2 * 300) = 168.4 m/s^2
So, the average acceleration is 168.4 m/s^2.
(ii) The time taken to accelerate from 20 km/h to 160 km/h can be determined using the equation:
time = (final velocity - initial velocity) / average acceleration
Substituting the values, we get:
time = (44.44 m/s - 5.56 m/s) / 168.4 m/s^2 = 0.25 seconds
So, it takes 0.25 seconds to accelerate from 20 km/h to 160 km/h.
(iii) The tractive force produced by the car to provide this acceleration can be determined using Newton's second law of motion:
force = mass * acceleration
Given that the mass of the racing car is 850 kg and the average acceleration is 168.4 m/s^2, we can calculate:
force = 850 kg * 168.4 m/s^2 = 143,440 N
So, the tractive force produced by the car to provide this acceleration is 143,440 N.
(iv) To determine the power output required to maintain a speed of 250 km/h, we need to consider the work done against friction and wind resistance.
The work done against friction and wind resistance is equal to the force multiplied by the distance traveled against it. So, the work done is:
work = force * distance
Given that the force is 1800 N and the distance is not provided, we cannot determine the work done directly. However, we can use the fact that work done is equal to the change in kinetic energy (KE):
work = ΔKE
The change in kinetic energy can be calculated as:
ΔKE = (1/2) * mass * (final velocity^2 - initial velocity^2)
Here, the mass is given as 850 kg, the final velocity is 250 km/h, and the initial velocity is not provided. Assuming the initial velocity is zero (as the car starts from rest), the equation becomes:
ΔKE = (1/2) * 850 kg * (250 km/h)^2
Converting the final velocity to m/s, we have:
ΔKE = (1/2) * 850 kg * (250 km/h * (1000 m/3600 s))^2
Calculating the value of ΔKE, we obtain:
ΔKE = 47,395,833.33 J
This work is done in a certain amount of time, which we can calculate as follows:
time = distance / final velocity
Here, the distance is not provided, but since the car is maintaining a speed, we can assume a distance of 1 meter for simplicity.
time = 1 m / (250 km/h * (1000 m/3600 s)) = 1.152 s
Now, we can calculate the power:
power = work / time
Substituting the values, we get:
power = 47,395,833.33 J / 1.152 s ≈ 41,140,912.76 W
Therefore, the power output required to maintain a speed of 250 km/h is approximately 41,140,912.76 Watts.