Assuming maximal power output, how long, in seconds, would it take a 1,535 kg car with a 128 hp engine to accelerate from 50 km/h to 102 km/h? (1 hp = 746 W)

To find out how long it would take for the car to accelerate from 50 km/h to 102 km/h, we can use the principles of work, power, and energy.

First, let's calculate the power output of the engine in watts. We are given that 1 horsepower (hp) is equal to 746 watts. So, the power output in watts would be:

Power (in watts) = 128 hp × 746 W/hp

Next, let's convert the initial and final velocities from km/h to m/s since we are working with SI units:

Initial velocity (v₁) = 50 km/h = (50 × 1000) / 3600 m/s
Final velocity (v₂) = 102 km/h = (102 × 1000) / 3600 m/s

Now, let's calculate the change in kinetic energy of the car:

Change in kinetic energy (ΔKE) = (1/2) × mass × ((v₂)² - (v₁)²)

where mass = 1,535 kg

Let's assume that the power output of the engine is the maximum power that it could generate, which means that all the power produced is utilized to accelerate the car. In this case, the time taken to accelerate can be calculated as the change in kinetic energy divided by the power output of the engine:

Time (t) = ΔKE / Power

Finally, we can substitute the given values into the formula to calculate the time:

Time (in seconds) = ((1/2) × 1,535 kg × ((v₂)² - (v₁)²)) / Power

Now, you can plug in the values and calculate the time required to accelerate the car from 50 km/h to 102 km/h.