Provided a racing car does not lose traction, the time taken by it to race from rest through a distance depends mainly on engine's power P. Derive the time t in terms of S and P, assuming that power is constant.

Explanation

To derive the time \( t \) taken by a racing car to race through a distance \( S \) in terms of the engine's power \( P \), we can follow these steps:

### Step 1: Understand the relationship between power, force, and velocity
Power \( P \) is defined as the rate of doing work, which can also be expressed in terms of force \( F \) and velocity \( v \):
\[ P = F \cdot v \]
Since the racing car is accelerating, we can express the force in terms of mass \( m \) and acceleration \( a \):
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