# Why Does the Acceleration of a Particle Need to Be Zero for Maximum Speed?

In summary, the velocity of particle P is given by two equations depending on the time interval. For 0≤t≤4, V={8t-3/2t²}, and for t>4, V={16-2t}. To achieve the greatest speed within the interval 0≤t≤4, the acceleration must be equal to zero, which can be visually understood by plotting the velocity-time curve as a parabola opening downward.
A particle P moves on the x-axis. At time t seconds the velocity of P is V m/s in the direction of x increasing?o
V is given by V={8t-3/2t²} for 0≤t≤4
Also V={16-2t} for t>4

Why does the acceleration have to equal zero to get the greatest speed of P in interval 0≤t≤4

This is probably best understood by plotting the velocity. Look at the maximum, and see what the slope is visually.

Roadtrip, post: 5499325, member: 596960"]A particle P moves on the x-axis. At time t seconds the velocity of P is V m/s in the direction of x increasing?o
V is given by V={8t-3/2t²} for 0≤t≤4
Also V={16-2t} for t>4

Why does the acceleration have to equal zero to get the greatest speed of P in interval 0≤t≤4
Plot v-t curve for t<4.It would be a parabola open downward.Velocity is maximum at maxima of the curve.Maybe now you can understand why acceleration would be zero.

## 1. What is mechanics/kinematic calculus?

Mechanics/kinematic calculus is a branch of physics that deals with the motion of objects and the forces that cause them to move. It involves using mathematical equations and principles to analyze and predict the motion of objects.

## 2. What are some common applications of mechanics/kinematic calculus?

Mechanics/kinematic calculus is used in various fields such as engineering, physics, and astronomy. It is used to design and analyze machines, predict the motion of celestial bodies, and understand the behavior of particles and fluids.

## 3. What are the fundamental principles of mechanics/kinematic calculus?

The fundamental principles of mechanics/kinematic calculus are Newton's laws of motion, which state that an object will remain at rest or in uniform motion unless acted upon by an external force, and the relationship between force, mass, and acceleration.

## 4. How is calculus used in mechanics/kinematic calculus?

Calculus is used to describe and analyze the motion of objects by calculating their position, velocity, and acceleration at different points in time. It allows us to understand how an object's motion changes over time and to make predictions about its future behavior.

## 5. What are some common mathematical equations used in mechanics/kinematic calculus?

Some common equations used in mechanics/kinematic calculus include the equations of motion (such as position, velocity, and acceleration), the laws of conservation of energy and momentum, and the equations for calculating forces (such as Newton's second law and the universal law of gravitation).

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