Question

A particle’s position, captured by a strobe camera, is shown below. The positions have been labeled times t0 through t8. The time intervals are equally separated?

Answer 1

The question involves calculations related to the position, velocity, and acceleration of a particle in physics, specifically finding the time when the particle crosses the origin, its displacement over a period, and determining its acceleration and position at different instances when the velocity is a function of time.

Step-by-step explanation:

Understanding Particle Motion

The question regards the motion of a particle along the x-axis and its position as a function of time, described by equations of motion in Physics. In part (a), to find the time when the particle crosses the origin, you would set the position function x(t) = 4.0 - 2.0t to zero and solve for t. In part (b), the displacement is the difference in position from t = 3.0 s to t = 6.0 s, which we find by calculating x(6) - x(3) using the given position function.

In consideration of velocity and acceleration, if a particle's velocity remains a constant 7.0 m/s, its acceleration as a function of time is zero since its velocity does not change. The position at various times is found by integrating the velocity function, or by using the formula x(t) = x0 + vt given the initial position x0 and the constant velocity v.

Finally, when dealing with velocity that varies with time, such as v(t) = A + Bt−1, acceleration is found by differentiating the velocity function with respect to time, and position is obtained by integrating the velocity over the given time, using any known initial positions to solve for constants in the position function.

Answer 2

No, the time intervals are not equally separated.

The strobe camera captures the particle's position at fixed time intervals. However, the particle is moving at different speeds throughout its motion. When the particle is moving slower, the distance between the captured positions is smaller. Conversely, when the particle is moving faster, the distance between the captured positions is larger.

In the image, you can see that the distances between the positions labeled t0, t1, and t2 are smaller than the distances between the positions labeled t3, t4, and t5. This indicates that the particle is moving slower at the beginning of its motion and faster towards the end.

Therefore, the time intervals between the captured positions are not equal. They are shorter when the particle is moving slower and longer when the particle is moving faster.