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 | | From: | sai yee | | Subject: | A Question | | Date: | 6 Jan 2005 02:26:45 -0800 |
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 | Given that the acceleration of a car is 7.5ms^-2
the deceleration of the car is 5ms^-2
What is the shortest time for car to travel 100m and stop at the end?
Can anyone help me please?
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| | From: | Barb Knox | | Subject: | Re: A Question | | Date: | Fri, 07 Jan 2005 14:49:57 +1300 |
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| In article ,
eeyias2003@yahoo.com.hk (sai yee) wrote:
>Given that the acceleration of a car is 7.5ms^-2
> the deceleration of the car is 5ms^-2
>
>What is the shortest time for car to travel 100m and stop at the end?
>
>Can anyone help me please?
Let Ta and Td be the times spent accelerating and decelerating,
respectively. Then the total time (your answer) is Ta + Td.
Since the velocity is 0 at both the beginning and the end,
Ta*7.5 - Td*5.0 = 0.
Solve this for Ta in terms of Td (or vice versa).
The distance travelled while accelerating is
1/2 * 7.5 * Ta^2,
and while decelerating is
1/2 * 5.0 * Td^2.
The sum of these two is 100, which (after substituting for Ta or Td) gives
you 1 equation in 1 unknown.
(BTW, the numbers are unrealistic. For one thing, a car with working brakes
decelerates faster than it accelerates, not vice versa.)
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