acceleration=-1/2x^2.at time t=0it is at x=1.0m and its velocity v=o.find the time when it reaches x=0.25 m
To find the time when the object reaches x = 0.25 m, we need to use the information given about acceleration, initial position, and initial velocity. Here's how you can find the answer step by step:
1. Start with the formula for displacement as a function of time under constant acceleration:
x = x0 + v0 * t + (1/2) * a * t^2
Where:
x = final position (0.25 m)
x0 = initial position (1.0 m)
v0 = initial velocity (0 m/s)
a = acceleration (-1/2 x^2)
t = time
2. Rewrite the formula using the given values:
0.25 = 1.0 + 0 * t + (1/2) * (-1/2 * x^2) * t^2
3. Simplify the equation:
0.25 = 1.0 - (1/4) * x^2 * t^2
4. Rearrange the equation to isolate t^2:
(1/4) * x^2 * t^2 = 1.0 - 0.25
(1/4) * x^2 * t^2 = 0.75
5. Divide both sides by (1/4) * x^2:
t^2 = (0.75) / ((1/4) * x^2)
6. Divide both sides by 0.75:
t^2 = (4/3) / (x^2)
7. Take the square root of both sides to solve for t:
t = sqrt((4/3) / (x^2))
Now, substitute x = 0.25 m into the equation to find the time when the object reaches x = 0.25 m:
t = sqrt((4/3) / (0.25^2))
t = sqrt(16 / (3 * 0.0625))
t = sqrt(16 / 0.1875)
t = sqrt(85.33333...)
t ≈ 9.232s (rounded to three decimal places)
Therefore, the time when the object reaches x = 0.25 m is approximately 9.232 seconds.