Question

Andrea, a 61.0 kg sprinter, starts a race with an acceleration of 3.300 m/s2. If she accelerates at that rate for 13.00 m and then maintains that velocity for the remainder of a 100.00 m dash, what will her time (in s) be for the race?

Answer 1

Answer:

$t=12.21s$

Explanation:

We calculate the time that Andrea spent while accelerating, using the following kinematic equation:

$v=v_0+at_1\\t_1=\frac{v}{a}(1)$

The final speed of Andrea in the first interval is given by:

$v^2=2ax\\v=\sqrt{2(3.3\frac{m}{s^2})(13m)}\\v=9.26\frac{m}{s}$

Using (1):

$t_1=\frac{9.26\frac{m}{s}}{3.3\frac{m}{s^2}}\\t_1=2.81s$

Then, Andrea is under an uniform motion. So, the time is given by:

$t_2=\frac{x}{v}\\t_2=\frac{100m-13m}{9.26\frac{m}{s}}\\t_2=9.40s$

Thus, the total time is:

$t=t_1+t_2\\t=2.81s+9.40s\\t=12.21s$

Answer 2

Explanation:

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