# Linear Motion - Particle Displacement

• IntegrateMe
In summary, the function v(t) = 9 - t^2 represents the velocity of a particle moving along the x-axis in m/sec, with t measured in seconds. Using analytic methods, we can determine the particle's direction of movement (to the right, to the left, or stopped), its displacement for the time interval 0 <= t <= 6, and the total distance traveled during this time. To solve, we can find the integration of dx = (9-t^2)*dt and equate it to zero to determine when the particle has zero displacement.
IntegrateMe
The function v(t) = 9 - t2 is the velocity in m/sec for a particle moving along the x-axis, where t is measured in seconds (t is greater than or equal to 0). Use analytic methods to solve:

(a) When the particle is moving to the right, to the left, and stopped.
(b) The particles displacement for 0 <= t <= 6 (<= means "less than or equal to")
(c) The total distance the particle traveled for 0 <= t <= 6

I'm going to be honest, i have no idea how to even start on the problem. Any help would be greatly appreciated.

v(t) = dx/dt = 9 - t^2.
So dx = (9-t^2)*dt.
Find the integration and equate it to zero. You will get t for which the displacement is zero.

## What is linear motion?

Linear motion, also known as rectilinear motion, is the movement of an object along a straight line. This type of motion occurs when all points on the object move the same distance in the same direction, resulting in a displacement.

## What is particle displacement?

Particle displacement is the change in position of a particle or object from its original location. It is a vector quantity and is measured in units of distance, such as meters or feet.

## What is the difference between distance and displacement?

Distance refers to the total length of the path traveled by an object, while displacement refers to the change in position of the object from its initial to final location. Distance has a scalar value, while displacement is a vector quantity with both magnitude and direction.

## What is the equation for calculating displacement?

The equation for calculating displacement is D = xf - xi, where D represents displacement, xf represents the final position, and xi represents the initial position. Displacement is often measured in meters (m) or feet (ft).

## What factors affect particle displacement in linear motion?

The factors that affect particle displacement in linear motion include the initial velocity of the object, the acceleration of the object, and the time it takes for the object to travel from its initial to final position. The mass and force applied to the object may also affect its displacement.

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