A muon (an elementary particle) enters a region with a speed of 5.00 ×10^6 m / s and then is sl

step 1 Okay, the speed is 5 times 10 to the 6th power meters per second. But the acceleration is negati

A muon (an elementary particle) enters a region with a speed...

A muon (an elementary particle) enters a region with a speed of $5.00 \times 10^{6} \mathrm{~m} / \mathrm{s}$ and then is slowed at the rate of $1.25 \times 10^{14} \mathrm{~m} / \mathrm{s}^{2}$. (a) How far does the muon take to stop? (b) Graph $x$ versus $t$ and $v$ versus $t$ for the muon.

A muon (an elementary particle) enters a region with a speed of $5.00 \times 10^{6} \mathrm{~m} / \mathrm{s}$ and then is slowed at the rate of $1.25 \times 10^{14} \mathrm{~m} / \mathrm{s}^{2}$.
(a) How far does the muon take to stop?
(b) Graph $x$ versus $t$ and $v$ versus $t$ for the muon.

Key Concepts

Uniform Acceleration

This concept refers to motion where the acceleration remains constant over time. In uniformly accelerated motion, the equations of motion can be directly applied because acceleration does not change, making it straightforward to calculate changes in velocity and position over time. This principle applies not only to speeding up but also to slowing down (deceleration), where acceleration is negative relative to the direction of motion.

Kinematic Equations

Kinematic equations relate the parameters of motion such as displacement, initial velocity, final velocity, acceleration, and time. The formulas, including v = v? + at and x = x? + v?t + ½at², allow for the direct calculation of one variable when the others are known under constant acceleration conditions. These equations are fundamental for solving problems involving the time it takes for an object to come to a stop and the distance it travels during that time.

Position versus Time Graph

A position versus time graph shows how the location of an object changes over the duration of its motion. For uniformly accelerated motion, this graph typically takes the shape of a parabola, reflecting the quadratic relationship between displacement and time. The curvature of the graph reveals information about the acceleration magnitude and the direction of the motion.

Velocity versus Time Graph

A velocity versus time graph plots how an object's speed and direction (velocity) change over time. Under uniform acceleration, such a graph is a straight line, where the slope of the line represents the constant acceleration. The point at which the graph crosses the time axis (v = 0) indicates the moment when the object comes to a complete stop. This graph provides a clear visual interpretation of the rate at which velocity changes.