Solution by hand step by step without integration if it available.

Given the acceleration pattern shown in Fig. below, $($a$)$ derive and plot the relationship between speed and

time and $($b$)$ calculate the total distance traveled during the $20$ second interval. At $t=0$ the vehicle was traveling

at $19k\frac{m}{h}.$

What is the safe stopping distance for a section of rural freeway with a design speed of $80m\frac{i}{h}on4\%$

upgrade? $($Assume $f=0\mathrm{.}348)$

A driver takes $3\mathrm{.}2$ s to react to a complex situation while traveling at a speed of $55m\frac{i}{h}.$ How far does the

vehicle travel before the driver initiates a physical response to the situation $($i$.$e$.,$ putting his foot on the brake$)?$

The driver of a vehicle travelling $50$ mph required $125$ ft to stop after he has applied the brakes. What is the

longitudinal slope if the coefficient of friction developed between tires and pavement is $0\mathrm{.}348?$

What minimum radius of curvature may be designed for safe operation of vehicles at $70$ mph if the maximum

rate of superelevation $($e$)$ is $6\%$ and the maximum coefficient of side friction $($f$)$ is $0\mathrm{.}10?$