Respuesta :
Explanation:
The given data is as follows.
Final velocity (v) = 8.62 m/s, Initial velocity ([tex]v_{o}[/tex]) = ?
time = 8.25 sec, distance (s) = 12.9 m
Hence, formula to calculate the initial velocity is as follows.
v = [tex]v_{o} + a \times t[/tex]
8.62 m/s = [tex]v_{o} + a \times 8.25 s[/tex]
[tex]v_{o}[/tex] = 8.62 m/s - 8.25a ......... (1)
Also, s = [tex]v_{o} \times t + \frac{1}{2}a \times t^{2}[/tex] ...... (2)
Therefore, substitute the value of [tex]v_{o}[/tex] from equation (1) into equation (2) as follows.
s = [tex]v_{o} \times t + \frac{1}{2}a \times t^{2}[/tex]
s = [tex]8.62 m/s - 8.25a \times t + \frac{1}{2}a \times t^{2}[/tex] ....... (3)
Now, putting the values of s and t into equation (3) as follows.
s = [tex]8.62 m/s - 8.25a \times t + \frac{1}{2}a \times t^{2}[/tex]
12.9 m = [tex](8.62 m/s - a \times 8.25sec) \times 8.25 s + \frac{1}{2}a \times (8.25 sec)^{2}[/tex]
a = 1.71 [tex]m/s^{2}[/tex]
Therefore, using equation (1) the value of initial velocity will be as follows.
[tex]v_{o}[/tex] = [tex]8.62 m/s - 8.25 sec \times a[/tex]
= [tex]8.62 m/s - 8.25 sec \times 1.71 m/s^{2}[/tex]
= -5.49 m/s
Thus, we can conclude that starting velocity of the car is -5.49 m/s.
