# Position Formula

A rectilinear movement is one whose trajectory follows a straight line. In addition, this movement is performed at constant acceleration. On the straight line we place an origin x_{0}, where there will be an observer who will measure the position x of the mobile at the instant t. The position x of the mobile can be related to time t by means of a polynomial function.

position = initial position+ initial velocity * time + 1/2 * acceleration * (time)^2

The equation is written:

x = x_{0} + v_{0}t + a*t^{2}/2

We have:

x = position

x_{0} = initial position

v_{0} = initial velocity

t = time

a = acceleration

Position Questions:

1) A body with an initial velocity of 8 m/s begins to accelerate in t = 0 at a rate of 6 m/s^{2}. What distance does it travel for the next 20 seconds from the instant it begins to accelerate?

Answer: To achieve the distance travelled use the equation described above. We define the initial position x_{0} = 0 m, because we want to know the distance from that point, v_{0} = 8 m/s, t = 20s and a = 6 m/s ^{2}.

x = (8 m/s)(20s)+(6 m/s^{2})(20 s)^{2}/2

x = 160 m + 1200 m

x = 1360 m.

2) A train travels at a constant speed of 50 m/s and passes a signal in red. 60 meters after passing the signal begins to slow down at a rate of 2 m/s^{2}. At what distance from the signal does it stop completely in 10 seconds?

Answer: To achieve the distance travelled use the equation described above. We have x_{0} = 60 m, v_{0} = 70 m/s, t = 20s and a = -2 m/s^{2}.

x = 60 m + (50 m/s)(10 s) + (-2 m/s^{2})(10 s)^{2}/2

x = 60 m + 500 m - 100 m

x = 460 m.

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