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