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Basic Rules of Differentiation
3. Techniques of Differentiation / Basic Rules of Differentiation / Problem 6
Problem 6

A car accelerates from rest along a straight road and its distance from the starting point is given by the equation S=54t2S=\frac54t^2, where SS is the distance in meters and tt is the time in seconds. If the car needs to reach a speed of 90 km/h90~\text{km/h} to safely merge onto a highway, how long will it take to reach this speed, and what distance will the car cover?

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