Respuesta :
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]
