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At the beginning of its route, a garbage truck accelerates at 10ms2 as it is driven down the road. By the end of the route, the truck's mass has quadrupled. If the truck's force remains constant, what is the truck's acceleration at the end of the route?
select one
- 2.5 m/s^2
- 10 m/s^2
- 20 m/s^2
- 5 m/s^2

Respuesta :

sam4040

Answer:

[tex]2.5\ m/s^2[/tex]

Step-by-step explanation:

Newton's Second Law: Force on a body is equal to the product of mass and acceleration of the centre of the mass of the body.

[tex]Force(F)=Mass(m)\times Acceleration(a)[/tex]

Initially:

[tex]Let\ mass=m\ kg\\\\acceleration=10\ m/s^2\\\\Force(F)=m\times 10=10m[/tex]

At the end of the road:

[tex]Let\ mass=4\times m\ kg\\\\acceleration=a\ m/s^2\\\\Force(F)=4m\times a=4ma[/tex]

[tex]Both\ forces\ are\ equal\\\\4ma=10m\\\\divide\ both\ the\ sides\ by\ m\\\\4a=10\\\\a=\frac{10}{4}\\\\a=2.5\ m/s^2[/tex]

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