John C.

asked • 11/14/17

What is its acceleration?

A car starts from a rest and rolls down a hill. The height of the hill is .3 km and the distance traveled by the car is 4.8 km. Dissipated energy is negligible. What is its acceleration?

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Arturo O. answered • 11/14/17

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In this problem, the acceleration is constant, and due only to gravity.  The acceleration down the plane is
 
a = -g sinθ  [down being negative]
 
sinθ = (0.3)/√(0.32 + 4.82) ≅ 0.06238
 
a = -(9.8 m/s2)(0.06238) = -0.611 m/s2
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Arturo O.

NOTE:  You can get the magnitude of the acceleration from kinematics:
 
v2 - (0)2 = 2ad
 
a = v2/(2d)
 
Get v2 from
 
(1/2)mv2 = mgh ⇒ v2 = 2gh = 2(9.8)(300) (m/s)2 = 5880 (m/s)2
 
d = √(3002 + 48002) m ≅ 4809 m
 
a = [5880 (m/s)2]/[2(4809 m)] ≠ 0.611 m/s2
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11/14/17

Arturo O.

In the last line above, I meant to say
 
a = [5880 (m/s)2]/[2(4809 m)] ≅ 0.611 m/s2
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11/14/17

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