中四力學

中四力學

2010-10-08 2:59 am

圖1 --> http://i670.photobucket.com/albums/vv68/blue2031/1-4.png

在時間t=0s﹐一艘小船從靜止開始沿一直線航行。圖1顯示該船從t=0至300s的速度與時間關係線圖。

*a 描述小船從t=0至300s的運動。

b 求小船在最初50s內的加速度。

c, 在圖2中﹐繪出小船從t=0至300s的加速度與時間關係線圖。

d, 求小船在最初50s內航行的距離。

e,一浮標位於小船起點前面900m處。試解釋小船在圖1所顯示的運動中會否經過該浮標。

圖2 -->http://i670.photobucket.com/albums/vv68/blue2031/2-5.png

2 在運動會上﹐美玲參加了100米短跑。她在t=0時起步並以勻加速度1.6ms-2跑了5s﹐然後以勻速率跑畢餘下路程。她在t=15s時到達終點。

a 求
i 美玲在t=5s時的速率；
ii 美玲在全程內的平均速率。

d 淑儀參加了同一項短跑。她首先以勻加速度1.5ms-2跑了6s﹐然後以勻速率跑畢餘下路程。

試解釋首先到達終點的是美玲還是淑儀。

回答 (1)

天同

2010-10-08 10:18 pm

✔ 最佳答案

(a) acceleration from 0 to 50s, constant velocity from 50 to 150s, deccelerate from 150 to 250s, then accelerate in the reverse direction from 250 to 300s.

(b) acceleration = 5/50 m/s2 = 0.1 m/s2
(c) straight line (at y = 0.1 m/s2) above axis from 1 to 50s , zero from 50 to 150s, straight line (at y = -0.05 m/s2) below x-axis from 150 to 300s

(d) Distance travelled = (1/2) x 5 x 50 m = 125 m
(e) Max distance travelled = (1/2) x [(150-50) + 250] x 5 m = 875 m
No, the boat will not pass the float, since the max distance travelled by the boat is only 875 metres.

.2. (a)(i) speed = 1.6 x 5 m/s = 8 m/s
(ii) Average speed = 100/15 m/s = 6.67 m/s

(d) Speed at 6s = 1.5 x 6 m/s = 9 m/s
Distance travelled in the first 6s = (1/2).x 9 x6 m = 27 m
Hence, time needed to cover the rest of the (100-27) m = 73 m
= 73/9 s = 8.11 s
Total time taken by 淑儀 = (6 + 8.11) s = 14.11 s

Therefore, 淑儀 will win the race because she takes only 14.11 s to finish the race, compared with 15s taken by 美玲

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中四 力學

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