A body moving with uniform acceleration has a velocity of 16.9 cm/s when its x coordinate is 3.1 cm. If its x coordinate 3.18 s later is -4.72 cm, what is the x-component of its acceleration?
To find the x-component of the acceleration, we can use the equations of motion.
We are given the initial velocity (v₀) as 16.9 cm/s, the initial x-coordinate (x₀) as 3.1 cm, the time interval (Δt) as 3.18 seconds, and the final x-coordinate (x) as -4.72 cm.
The equation that relates displacement, initial velocity, time, and acceleration is:
x = x₀ + v₀t + (1/2)at²
Plugging in the given values, we get:
-4.72 cm = 3.1 cm + (16.9 cm/s)(3.18 s) + (1/2)a(3.18 s)²
Now, we can solve this equation for the x-component of acceleration (a).