An automobile travelling on a straight, level road has an initial speed v when the brakes are applied. in coming to rest with a constant acceleration, it travels a distance x. how far would the automobile travel in coming to rest if it had the same acceleration but an initial speed 2v ? a. 1/4x. b. 1/2x. c. x. d. 2x. e. 4x.

a. 1/4X

Explanation:

As this is an uniformly accelerated rectilinear motion, we are able to use the following formulas, that link acceleration (a), speed (V), time (t) and distance (X):

V = at and X = 1/2at²

Combining both formulas, we get: V = √(2aX )

Now, if we consider both situations stated on this problem :

-Condition 1 : X₁ , V1₁

-Condition 2: X₂, V₂ = 2V₁

Finally : V₁ = √(2aX1 )

V2 = 2V1 = √(2aX2 )

Dividing both equations:

V1/2V1 = √[(2aX1)/(2aX2) ]

1/2 = √[(2aX1)/(2aX2)]   ⇒ (1/2)² = X₁/X₂ ⇒ 1/4 = X₁/X₂  

X2 = 1/4*X1  

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