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A sprinter can accelerate with constant acceleration for 3.40 s before reaching top speed He can run the 100-meter dash in 10 s?
Wiki User
∙ 9y ago
1/2a(3.4)^2+[3.4a(a=0)](6.6)=100
[] is Vi and a in this case is 0 at it stops to accelerate when it gets to 3.4s
so a=100/(.5)(3.4)^2....=17.30
now Vf=(3.4*17.30)+17.30(6.6)...=173.01
Wiki User
∙ 9y ago
Wiki User
∙ 9y agoUsing the information in the question, of course he can!
You haven't specified what magnitude of acceleration he can maintain for 3.4 seconds, so the
whole effort is a piece-o'-cake, and anybody who can accelerate for 3.4 seconds can do it.
For example, since you've imposed no restrictions on the magnitude of acceleration, let's
assume that he accelerates for 3.4 seconds at the rate of 17.3 meters per second-squared,
to a maximum speed of 58.8 meters per second. His average speed during that time is
58.8/2 = 29.4 meters per second, and at that average speed, he covers exactly 100 meters
in 3.4 seconds ... crossing the finish-line and shattering all past and future world records
just as he reaches his top speed and stops accelerating.
On the other hand, if he had a rough night, and all he really wants to do is finish 100 meters
in 10 seconds and go lie down, then he need only accelerate at a leisurely 2 meters per second-
squared for 10 seconds, reaching the top speed of 20 meters per second. Then his average speed
is 10 meters per second, putting him at the 100-meters mark after 10 seconds.
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