Calculating Particle's Acceleration

What is the acceleration of the particle that moves from x = 10m to x = 50m with constant acceleration along the x-axis, and a final speed of 10 m/s?

The correct response is x23.

Understanding the Problem

In this scenario, we have a particle moving along the x-axis with a constant acceleration. The particle starts at position x = 10m and ends at x = 50m with a final speed of 10m/s. We are asked to find the acceleration of the particle during this motion.

Using the Kinematic Equations

To determine the acceleration of the particle, we can use the kinematic equations of motion. One of the key equations that relates acceleration, initial velocity, final velocity, and displacement is:

v^2 = u^2 + 2as

where:

v = final velocity = 10 m/s

u = initial velocity (which is not given)

a = acceleration

s = displacement = 50m - 10m = 40m

Solving for Acceleration

Plugging in the given values into the kinematic equation:

10^2 = u^2 + 2 * a * 40

100 = u^2 + 80a

u^2 = 100 - 80a

Since the particle's final velocity is 10m/s, we know that the initial velocity is also a component of this equation, but it cancels out when calculating the acceleration. Therefore, we can focus on solving for acceleration only.

Substitute the given final velocity into the equation to solve for acceleration:

100 = 100 - 80a

0 = -80a

a = 0

Conclusion

The acceleration of the particle is 0. This indicates that the particle moves with a constant velocity, not changing its speed during the motion from x = 10m to x = 50m. The null value for acceleration signifies that there is no change in the particle's velocity, maintaining a steady speed of 10m/s throughout the displacement.