A car accelerates uniformly in a straight line from rest at the rate of 2.3 m/s2 . a. What is the speed of the car after it has traveled 55 m? b. How long does it take the car to travel 55 m?

Answer:The speed of the car after it's traveled 55 m is 15.9 m/s and it takes it 6.92 seconds to travel.Step-by-step explanation:Since the acceleration is uniform, we can calculate the distance the car travels x using the following equation:(1) [tex]x=v_m*t[/tex]being t the time it takes to travel and [tex]v_m[/tex] it's mean velocity which is given by:[tex]v_m=\frac{v_0+a*t}{2}[/tex]where [tex]v_0[/tex] is the initial velocity (0 in this case). Replacin this in (1):(2) [tex]x=\frac{a*t}{2}*t\\x=a*\frac{t^2}{2}[/tex]we already have the distance traveled x and the acceleration a so we can calculate t using (2):[tex]t^2=\frac{2x}{a}\\t=\sqrt{\frac{2x}{a}}\\t=\sqrt{\frac{2*55m}{2.3\frac{m}{s^2}}}\\t=6.92s\\[/tex]Now we use this time to calculate the final velocity v[tex]v=a*t\\v=2.3\frac{m}{s^2}*6.92s\\v=15.9\frac{m}{s}[/tex]