A 1000 kg car can accelerate from rest to v = 85 km/hr in a time t = 7.4s.
If, instead the power of the car is smaller by a factor of .4 and the car accelerates for the same amount of time, by what factor will the maximum speed decrease?
To find the factor by which the maximum speed will decrease, we need to compare the power of the car in both scenarios.
The power (P) of a car can be calculated by the equation:
P = (1/2) * m * v^2 / t
where m is the mass of the car, v is the velocity, and t is the time taken to accelerate.
In the first scenario, the power (P1) can be calculated as:
P1 = (1/2) * 1000 kg * (85 km/hr)^2 / 7.4s
In the second scenario, the power (P2) is smaller by a factor of 0.4, so we can calculate it as:
P2 = 0.4 * P1
Since both scenarios have the same acceleration time, we can equate the two power equations:
P1 = P2
Substituting the values:
(1/2) * 1000 kg * (85 km/hr)^2 / 7.4s = 0.4 * [(1/2) * 1000 kg * (v2)^2 / 7.4s]
Simplifying the equation:
(85 km/hr)^2 = 0.4 * (v2)^2
Now, we need to find the factor by which the maximum speed will decrease. Let's call it "x".
(85 km/hr)^2 = 0.4 * (v2)^2
Dividing both sides by 0.4:
(85 km/hr)^2 / 0.4 = (v2)^2
Square rooting both sides:
85 km/hr * (1/sqrt(0.4)) = v2
Calculating the right-hand side:
85 km/hr * 1/sqrt(0.4) ≈ 107.124 km/hr
Therefore, the maximum speed in the second scenario will be approximately 107.124 km/hr.
The factor by which the maximum speed will decrease is given by:
Factor = Initial speed / Final speed
= 85 km/hr / 107.124 km/hr
Calculating:
Factor ≈ 0.793
Therefore, the maximum speed will decrease by a factor of approximately 0.793 in the second scenario.