Final answer:
The acceleration of an object traveling along the x-axis from x=6.0 m to x=10 m, with a change in velocity from +10 m/s to +15 m/s, is calculated using a kinematic equation. It is found to be 15.625 m/s², which conflicts with the student's answer of 16 m/s².
Step-by-step explanation:
The question is asking us to determine the acceleration of an object that is moving along the x-axis with varying velocities at different positions. To find the acceleration, we can use the kinematic equation:
v^2 = u^2 + 2as,
where
v is the final velocity,
u is the initial velocity,
a is the acceleration, and
s is the displacement.
Given that the velocity changes from +10 m/s to +15 m/s and the displacement (x) changes from 6.0 m to 10 m, the values are:
u = +10 m/s (initial velocity),
v = +15 m/s (final velocity),
s = 10 m - 6 m = 4 m (displacement).
Plugging these into the equation, we get:
(+15 m/s)^2 = (+10 m/s)^2 + 2 * a * 4 m,
225 m^2/s^2 = 100 m^2/s^2 + 8a m/s^2,
125 m^2/s^2 = 8a m/s^2,
a = 125 m^2/s^2 / 8 m/s^2,
a = 15.625 m/s^2.
The calculated acceleration is 15.625 m/s^2, rather than the answer provided by the student which is 16 m/s^2. It could be a typing error or a rounding off.