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 x0, 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 = x0 + v0t + a*t2/2
We have:
x = position
x0 = initial position
v0 = 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/s2. 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 x0 = 0 m, because we want to know the distance from that point, v0 = 8 m/s, t = 20s and a = 6 m/s 2.
x = (8 m/s)(20s)+(6 m/s2)(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/s2. 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 x0 = 60 m, v0 = 70 m/s, t = 20s and a = -2 m/s2.
x = 60 m + (50 m/s)(10 s) + (-2 m/s2)(10 s)2/2
x = 60 m + 500 m - 100 m
x = 460 m.
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