Finding the position at a change in direction

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Homework Statement

A particle moving along a straight line with constant acceleration starts its motion at t = 0. The particle is observed to change the direction of motion at t = 4 s, and when t = 10 s it reaches the position of −2 m with a −2.4 m/s velocity measured from a chosen reference frame. Find the position of the particle when it changes its direction of motion.
Ans: 5.2 m

Homework Equations

The Attempt at a Solution

 

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For the first part, when t = 4s, we can use the equation: x = x0 + v0t + ½at² where x0 = 0 (initial position), v0 = 0 (initial velocity) and a = ? (acceleration). Plugging in the values, x = 0 + 0 + ½at² x = ½at² For the second part, when t = 10s, we can use the equation: x = x0 + v0t + ½at² where x0 = -2m (position), v0 = -2.4 m/s (velocity) and a = ? (acceleration). Plugging in the values, x = -2 + (-2.4)10 + ½at² Now, we have two equations with one unknown, acceleration. Subtracting them gives us: ½at² - ½at² = -2 + 2.4(10) Therefore, a = 24 / 8 a = 3 m/s² Now, plugging in a = 3 m/s² in the first equation, when t = 4s, x = 0 + 0 + ½(3)(4²) x = 0 + 0 + 24 x = 24 m Therefore, the position of the particle when it changed its direction of motion was 24 m.