Question: Many car companies are performing research on collision avoidance systems. A small prototype applies engine braking that decelerates the vehicle according to the relationship a

Many car companies are performing research on collision avoidance systems. A small prototype applies engine braking that decelerates the vehicle according to the relationship a = -k√t, where a and t are expressed in m/s² and seconds, respectively. The vehicle is travelling 20 m/s when its radar sensors detect a stationary obstacle. Knowing that it takes the prototype vehicle 4 seconds to stop, determine

(a) Expressions for its velocity and position as a function of time,

(b) How far the vehicle travelled before it stopped.

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