acceleration problem

Zidane

2010-02-02 9:08 pm

I thought of a question, and want to know how to calculate it:

Tom finishes 100m in 10s, assume he accelerate his speed from 0 to his top speed in 30m, and then he keeps his speed unchange till the end of 100m.
I want to find :
1. his accleration speed of the first 30m
2. his speed of the remaining 70m

Is it possible to find out the solution to the above questions only based on this information? If yes, how to calculate?

thank you

回答 (1)

天同

2010-02-02 10:11 pm

✔ 最佳答案

Let T be the elapsed time for Tom to run the first 30 m (i.e. the time to reach top speed), and V be his top speed.

For the first 30 m, using equation of motion: s = (1/2)(u+v)t
with u = 0 m/s, t = T, v = V, s = 30 m
30 = VT/2
i.e. VT = 60 m

Since Tom remains at speed V for the rest 70 m in a time interval of (10-T) s,
hence, 70 = V(10-T)
i.e. 70 = 10V - VT = 10V - 60
hence, V = (70+60)/10 m/s = 13 m/s

To find the acceleration, use equation of motion: v^2 = u^2 + 2.a.s
with v = 13 m/s, u = 0 m/s, s = 30 m, a = ?
13x13 = 2a(30)
i.e. a = 169/60 m/s2 = 2.82 m/s2
,

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