A car can go from 0 to 85 km/h in 10 s. If the engine delivered twice the power, how many seconds would it take?
To solve this problem, we can use the concept of power and its relationship with acceleration. The power delivered by an engine is directly proportional to the acceleration it produces.
First, let's calculate the initial acceleration of the car based on the given information. We can use the formula for average acceleration:
acceleration = (final velocity - initial velocity) / time
Given that the initial velocity is 0 km/h and the final velocity is 85 km/h, and the time is 10s, we can plug these values into the equation to find the acceleration:
acceleration = (85 km/h - 0 km/h) / 10 s
acceleration = 85 km/h / 10 s
acceleration = 8.5 km/h/s
Now, let's consider the case where the engine delivers twice the power. Since power and acceleration are directly proportional, doubling the power would result in double the acceleration.
Therefore, the new acceleration would be:
new acceleration = 2 * 8.5 km/h/s
new acceleration = 17 km/h/s
Now, we can calculate the time it would take for the car to reach the same final velocity of 85 km/h with this new acceleration.
Using the same formula as before:
time = (final velocity - initial velocity) / acceleration
Plugging in the values:
time = (85 km/h - 0 km/h) / 17 km/h/s
time = 85 km/h / 17 km/h/s
time = 5 seconds
Thus, if the engine delivered twice the power, it would take 5 seconds for the car to go from 0 to 85 km/h.