$7.$ Consider a $180$ deg curve with the racecar following the path described by a clothoid. Assume the track has sufficient width and a straight away entrance and exit that the clothoid fits. The inner radius of the curve is $20$ ft$.$ If the g$-$g$-$ diagram is circular with maximum g $=1.,$ determine the distance, velocity and acceleration curves $($tangential and normal$)$ versus time so the driver remains on the max g$-$g envelope.