Answer:
The car will travel 541.67 m
Explanation:
Uniform Acceleration
When an object changes its velocity at the same rate, the acceleration is constant.
The relation between the initial and final speeds is:
[tex]v_f=v_o+a.t[/tex]
Where:
vf = Final speed
vo = Initial speed
a = Constant acceleration
t = Elapsed time
The acceleration can be computed by solving for a:
[tex]\displaystyle a=\frac{v_f-v_o}{t}[/tex]
And the distance traveled is calculated as follows:
[tex]\displaystyle x=v_o.t+\frac{a.t^2}{2}[/tex]
The car travels during a time of t=30 s, and its speed changes from vo=50 Km/h to vf=80 Km/h.
Converting the speeds to m/s:
vo=50 Km/h * 1000/3600 = 13.89 m/s
vf=80 Km/h * 1000/3600 = 22.22 m/s
Both numbers are shown with a 2-decimal precision but they will be used with higher accuracy in further calculations.
Calculating the acceleration:
[tex]\displaystyle a=\frac{22.22-13.89}{30}[/tex]
[tex]a = 0.28\ m/s^2[/tex]
Now for the distance:
[tex]\displaystyle x=13.89*30+\frac{0.28.30^2}{2}[/tex]
[tex]x=416.67\ m+125\ m[/tex]
x = 541.67 m
The car will travel 541.67 m
