Answer:
The auto is moving at 38.9 m/s
The auto took 45 seconds to travel the 1033 m
Explanation:
Constant Accelerated Motion
it's a type of motion in which the velocity of an object changes uniformly in time.
The relationship between initial and final speeds is calculated by the equation:
[tex]v_f=v_o+at\qquad\qquad [1][/tex]
Where a is the constant acceleration, vo the initial speed, vf the final speed, and t the time.
Another useful equation allows us to calculate the distance x traveled by the object:
[tex]\displaystyle x=v_o.t+\frac{a.t^2}{2}\qquad\qquad [2][/tex]
(a)
Solving [1] for t and substituting into [2] we find the equation:
[tex]v_f^2=v_o^2+2ax[/tex]
This last equation will be used to solve the first part of the problem which gives the initial speed of vo=7 m/s, the uniform acceleration as a=0.71 m/s^2 and the distance traveled as x=1033 m, thus substituting:
[tex]v_f^2=7^2+2(0.71)(1033)[/tex]
[tex]v_f^2=49+1466.86=1515.86[/tex]
Thus:
[tex]v_f=\sqrt{1515.86}=38.9[/tex]
[tex]v_f=38.9 m/s[/tex]
The auto is moving at 38.9 m/s
(b)
To calculate the time, we solve [1] for t:
[tex]\displaystyle t=\frac{v_f-v_o}{a}[/tex]
[tex]\displaystyle t=\frac{38.9-7}{0.71}=45[/tex]
The auto took 45 seconds to travel the 1033 m
