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?

To solve this problem, we can use the equations of motion and the concept of work and power.

(i) The average acceleration can be calculated using the equation:

Average Acceleration = (Change in velocity) / (Time taken)

Given that the car accelerates from 20 km/h to 160 km/h, we can convert the velocities to m/s:

Initial velocity (u) = 20 km/h = (20 * 1000) / (60 * 60) m/s = 5.56 m/s
Final velocity (v) = 160 km/h = (160 * 1000) / (60 * 60) m/s = 44.44 m/s

Change in velocity = v - u = 44.44 - 5.56 = 38.88 m/s

We are not given the time taken directly, but we are given the distance.

(ii) To calculate the time taken, we can use the equation:

Distance = (Initial velocity * Time) + (0.5 * Average Acceleration * Time^2)

We rearrange this equation to solve for time:

Time = (Final velocity - Initial velocity) / (Average Acceleration)

Given that the distance is 300 meters, Average Acceleration =? and Initial velocity = 5.56 m/s, we can substitute these values into the equation to find the time taken.

(iii) The tractive force produced by the car is given by the equation:

Net Force = Mass * Average Acceleration

Given that the mass of the car is 850 kg, we can calculate the tractive force by substituting the values into the equation.

(iv) To find the power output required to maintain a speed of 250 km/h, we need to calculate the work done against friction and wind resistance. The power is equal to the rate at which work is done:

Power = Work / Time

The work done against friction and wind resistance is given by:

Work = Force * Distance

Given that the friction and wind resistance are 1800 N and the distance traveled is not mentioned, we cannot directly calculate the power output without this information. Please provide the distance traveled at a speed of 250 km/h, and we can assist you further.

To solve this problem, we will use the formulas of physics, specifically those related to force, acceleration, and power.

(i) The average acceleration can be calculated using the equation:

acceleration = (final velocity - initial velocity) / time

We need to convert the initial and final velocities from km/h to m/s, and the distance from meters to meters:

initial velocity = 20 km/h = (20 * 1000) / 3600 = 5.56 m/s
final velocity = 160 km/h = (160 * 1000) / 3600 = 44.44 m/s

Plugging the values into the formula:

acceleration = (44.44 m/s - 5.56 m/s) / time

(ii) To find the time taken to accelerate from 20 km/h to 160 km/h, we rearrange the formula from part (i):

time = (final velocity - initial velocity) / acceleration

(iii) To determine the tractive force produced by the car, we need to account for the frictional forces and wind resistance. The net force is given by the equation:

net force = mass * acceleration + frictional forces + wind resistance

Given: mass = 850 kg, frictional forces + wind resistance = 800 N

tractive force = net force - frictional forces - wind resistance

(iv) To find the power output required to maintain the speed of 250 km/h, we need to calculate the force required to overcome friction and wind resistance, and then multiply it by the velocity. The net force under these conditions is given by:

net force = frictional forces + wind resistance

Given: frictional forces + wind resistance = 1800 N

power = force * velocity

Let's now calculate the values using the given information.

(i) Average acceleration:

acceleration = (44.44 m/s - 5.56 m/s) / time

(ii) Time taken to accelerate:

time = (44.44 m/s - 5.56 m/s) / acceleration

(iii) Tractive force:

tractive force = (mass * acceleration) + frictional forces + wind resistance

(iv) Power output required to maintain 250 km/h:

power = (frictional forces + wind resistance) * velocity