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14 May, 10:02

A sprinter starts from rest and accelerates to her maximum speed of 10.5 m/s in a distance of 11.0 m. (a) What was her acceleration, if you assume it to be constant? 0 Incorrect: Your answer is incorrect. Units are required for this answer. seenKey 5.01 m/s^2 (b) If this maximum speed is maintained for another 96.3 m, how long does it take her to run 107.3 m?

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  1. 14 May, 11:44
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    a) a=5.01m/s^2

    b) t=11.26s

    Explanation:

    A body that moves with constant acceleration means that it moves in "a uniformly accelerated movement", which means that if the velocity is plotted with respect to time we will find a line and its slope will be the value of the acceleration, it determines how much it changes the speed with respect to time.

    When performing a mathematical demonstration, it is found that the equations that define this movement are as follows.

    Vf=Vo+a. t (1)

    {Vf^{2}-Vo^2}/{2. a} = X (2)

    X=Xo + VoT+0.5at^{2} (3)

    X = (Vf+Vo) T/2 (4)

    Where

    Vf = final speed

    Vo = Initial speed

    T = time

    A = acceleration

    X = displacement

    In conclusion to solve any problem related to a body that moves with constant acceleration we use the 3 above equations and use algebra to solve

    to solve the question a, we can use the ecuation number 2

    Vo=0

    Vf=10.5 m/s

    x=11m

    {Vf^{2}-Vo^2}/{2. a} = X

    {Vf^{2}-Vo^2}/{2. x} = a

    {10.5^{2}-0^2}/{2x11} = a

    a=5.01m/s^2

    to find the time we can use the ecuation number 1

    Vf=Vo+a. t

    t = (Vf-Vo) / a

    t = (10.5-0) / 5.01=2.09s

    part b

    in this case the spees is constant, so the movement is defined by the following ecuation

    X=VT

    t=x/v

    t=96.3/10.5=9.17s

    to find the total time we sum the times when the speed is constant and when the acceleration is constan

    t=9.17+2.09

    t=11.26s
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