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A truck passes point A on a straight level road with a constant velocity of 12 m/s. At the same instant, an automobile starts from rest at point A and travels in the same direction as the truck with a constant acceleration of 1.8 m/s2. How long a time does the automobile take to pass the truck from the instant it starts at point A?

Respuesta :

Answer:

[tex]t = 13.3 s[/tex]

Explanation:

Let the car will overtake the truck after time "t" seconds

so here we can say that after time "t" seconds the distance covered by the car will be same as that of distance covered by truck

So we have

[tex]d_{car} = d_{truck}[/tex]

so we have

[tex]d_{truck} = 12 t[/tex]

[tex]d_{car} = \frac{1}{2}(1.8 m/s^2) t^2[/tex]

so now we have

[tex]12 t = 0.9 t^2[/tex]

[tex]t = 13.3 s[/tex]

The rate of change of displacement of the body is known as the velocity of that body. The time does the automobile take to pass the truck will be 13.35 second.

What is velocity?

The rate of change of displacement of the body is known as the velocity of that body. Its unit is m/sec.

Allow the automobile to pass the truck after "t" seconds.

So, after "t" seconds, the distance reached by automobile will be the same as the distance covered by the truck.

[tex]d_{car}= d_{truck}[/tex]

As we know that distance is equal to the product of velocity and time.

v is the velocity of truck = 12m/sec.

[tex]d_{truck}= 12t[/tex]

As the car is moving with constant acceleration and zero initial velocity

u=0

a is the acceleration of car= 1.8m/sec²

[tex]\rm {S=ut+\frac{1}{2} at^2[/tex]

[tex]\rm {S=\frac{1}{2} at^2[/tex]

[tex]\rm {d_{car}=\frac{1}{2} (1.8)t^2[/tex]

[tex]d_{car}= d_{truck}[/tex]

[tex]\rm \frac{1}{2} (1.8)t^2= 12t[/tex]

[tex]0.9t^2= 12t\\\\t=13.35 sec.[/tex]

Hence the time does the automobile take to pass the truck will be 13.35 second.

To learn more about the velocity refer to the link;

https://brainly.com/question/862972