Physics Problem

2008-08-15 1:14 pm

A ferry travels 12 km in a straight line. It starts from rest and accelerates to its maximum speed. Upon reaching the maximum speed it starts to slow down. If the magnitude of acceleration is 4 times greater than the decceleration, find the distance travelled during the acceleration and decceleration parts of the trip.

Please answer with detailed steps and explainations. Thanks.

回答 (1)

用戶19865

2008-08-15 8:23 pm

✔ 最佳答案

Seperate the 12km travelling distance into two parts, the acceleration stage (stage 1) and deceleration stage (stage 2)

Assume the acceleration in stage 1 (with displacement=S1) be 4a, than the acceleration in stage 2 (with displacement =S2) will be -a (due to the oppose direction of force and the travelling direction).

then,
stage 1: by v²=u²+2as, we can see, as the ferry's initial speed is zero, v²=8aS1
stage 2: also by v²=u²+2as, we have 0=v²-2aS2, as it finally stops

therefore, we have
v²=8aS1-------------(1)
0=v²-2aS2-----------(2)
S1+S2=12km----------(3)

Sub (1) into (2),
aS2=4aS1
S2=4S1
USing (3),
S1=2.4km, S2=9.6km

distance travelled during the acceleration is 2.4km
distance travelled during the decceleration is 9.6km

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