A car moves with a velocity of 54km/h to a velocity of 72lm/h for 5 minutes. determine the distance covered

Answer:

The distance covered is 5250 meters

Explanation:

Motion With Constant Acceleration

It's a type of motion in which the velocity of an object changes uniformly in time.

The change of velocities is given by the following equation :

[tex]v_f=v_o+at\qquad\qquad [1][/tex]

Where:

a   = acceleration

vo = initial speed

vf  = final speed

t    = time

The distance traveled by the object is given by:

[tex]\displaystyle x=v_o.t+\frac{a.t^2}{2}\qquad\qquad [2][/tex]

Solving [1] for a:

[tex]\displaystyle a=\frac{v_f-v_o}{t}[/tex]

The car changes its speed from vo=54 Km/h to vf=72 Km/h in t=5 minutes. Let's convert all to meters and seconds.

vo=54 Km/h * 1000/3600 = 15 m/s

vf=72 Km/h * 1000/3600 = 20 m/s

t = 5 min * 60 = 300 s

Now we calculate the acceleration:

[tex]\displaystyle a=\frac{20-15}{300}[/tex]

[tex]\displaystyle a=\frac{5}{300}[/tex]

[tex]a=0.0167\ m/s^2[/tex]

Now for the distance:

[tex]\displaystyle x=15*300+\frac{0.0167*300^2}{2}[/tex]

[tex]\displaystyle x=4500+750=5250[/tex]

x = 5250 m

Note: We have shown only some of the decimals for the acceleration, but we have used all the decimals stored in the calculator to present accurate results.

The distance covered is 5250 meters

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