MHB Engineering Mechanics: car speeding up

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A car accelerates uniformly from rest, passing three electric posts spaced 360 meters apart. It takes 10 seconds to travel from the first to the second post and 6 seconds from the second to the third post. The distance from the starting point to the first post is represented as 'd', with equations derived from the car's motion used to solve for 'd'. The equations include the initial distance formula and the distances covered to each subsequent post, incorporating time and acceleration. The problem requires solving a system of equations to find the value of 'd'.
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A car starting from rest picks up at a uniform rate and passes three electric post in succession. The post are spaced 360 m apart along a straight rod. The car takes 10 seconds to travel from the first post to the 2nd post and tales 6 seconds to go from the 2nd post to the 3rd post. Determine the distance from the starting point to the first post.
 
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let $d$ be the distance from the starting point to the first post, $t$ be the time it takes to reach the first post from rest, and $a$ be the magnitude of the uniform acceleration.

$d = \dfrac{1}{2}at^2$

$d+360 = \dfrac{1}{2}a(t+10)^2$

$d+720 = \dfrac{1}{2}a(t+16)^2$

solve the system for $d$
 
skeeter said:
let $d$ be the distance from the starting point to the first post, $t$ be the time it takes to reach the first post from rest, and $a$ be the magnitude of the uniform acceleration.

$d = \dfrac{1}{2}at^2$

$d+360 = \dfrac{1}{2}a(t+10)^2$

$d+720 = \dfrac{1}{2}a(t+16)^2$

solve the system for $d$
Thank you
 
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