1100 kg car accelerates from rest reaching distance of 139 m in 8.7 sec determine average power in KW your answer to 2 decimal places?
1. find average acceleration, a
Vi=0
S=(1/2)at^2
139 m =(1/2)a(8.7²)
a=3.6729 m/s²
2. Find work done, W
a. using F=ma,
W = F*S = ma*S
where m=1100 kg, S=139 m, a=3.6729 m/s²
or
b. using energy (neglect loss)
final velocity, Vf = at
where t=8.7 s
final energy
=(1/2)m*Vf²
3. Find power = W/time in watts
1 KW = 1000 W.
To determine the average power, we can use the equation:
P = (W / t)
where P is the power, W is the work done, and t is the time taken.
First, we need to find the work done. The work done is given by the equation:
W = Fd
where F is the force applied and d is the distance covered.
To find the force applied, we can use Newton's second law of motion:
F = ma
where m is the mass of the car and a is its acceleration.
Given:
Mass of the car (m) = 1100 kg
Distance covered (d) = 139 m
Time taken (t) = 8.7 s
First, let's find the acceleration:
Using the formula:
a = (d - 0.5 * at^2) / t^2
Substituting the values, we get:
a = (139 - 0.5 * a * 8.7^2) / 8.7^2
Simplifying the equation, it becomes a quadratic equation:
0.5 * a * 8.7^2 + a * 139 - 139 * 8.7^2 = 0
Solving this quadratic equation, we find that the acceleration is approximately 3.28 m/s^2.
Now, let's find the force applied:
Using Newton's second law of motion:
F = ma
Substituting the values, we get:
F = 1100 * 3.28
So, the force applied is approximately 3608 N.
Finally, let's find the work done:
Using the formula:
W = Fd
Substituting the values, we get:
W = 3608 * 139
So, the work done is approximately 501,112 J.
Now, let's calculate the average power:
Using the formula:
P = W / t
Substituting the values, we get:
P = 501112 / 8.7
Calculating this, the average power is approximately 57,583.16 W or 57.58 kW (rounded to two decimal places).
Therefore, the average power of the car is approximately 57.58 kW.