# Motion Along a Straight Line

## Average Acceleration

Average Acceleration Average Acceleration Average acceleration is the ratio of a change in velocity 6,’ to the time interval dt in which the change occurs.

## Instantaneous Velocity

Instantaneous Velocity Instantaneous Velocity The instantaneous velocity (or simply velocity) , of a moving particle is where dx and dt are defined by Eq. 2-2. The instantaneous velocity (at a particular lime) may be found as the slope (at that particular time) of the graph of x versus t. Speed is the magnitude of instantaneous velocity.

## Average Speed

Average Speed Average Speed The average speed S of a particle during a time interval dt depends on the total distance the particle moves in that time interval:

## Average Velocity

Average Velocity Average Velocity When a particle has moved from position XI to X2 during a time interval dt = t2 – tl, its average velocity during that interval is. The algebraic sign of v indicates the direction of motion (v is a vector quantity). Average velocity does not depend on the actual distance a particle moves, but instead …

## Displacement

Displacement Displacement The displacement  of a particle is the change in its position: Displacement is a vector quantity. It is positive if the particle has moved in the positive direction of the x axis. and negative if the particle has moved in the negative direction.

## Position

Position Position The position x of a particle on an x axis locates the particle with respect to the origin, or zero point, of the axis. The position is either positive or negative, according to which side of the origin the particle is on, or zero if the particle is at the origin. The positive direction on an axis …

## PROBLEM SOLVING TACTICS

PROBLEM SOLVING TACTICS Tactic 7: Meanings of Minus Signs In many answers emerged automatically with minus signs. It is important to know what these signs mean. For these two falling-body problems, we established a vertical axis (the y axis) and we chose-quite arbitrarily- its upward direction to be positive. We then chose the origin of the y axis (that is, …

## Sample Problem

Sample Problem A  pitcher tosses a baseball up along a y axis, with an initial speed of 12 m/s. (a) How long does tlie ball.take to reach its maximum height? SOLUTION: One Key Idea here is that once the ball leaves the pitcher and before it returns, its acceleration is the free-fall acceleration       …

## Motion Along a Straight Iine

Motion Along a Straight line have known valves.We find Note that Munday’s dispiacement y – Yo is a negative quantity Munday fell down, in the negative direction of the y axis (he did  not fall up l). Also note that 48/4.9 has two square roots: 3.1 and – 3.1. Here we choose the positive root because Munday …

## Sample Problem

Sample Problem Let us return to the opening story about Dave Munday’s Niagara free fall in a steel ball. He fell 48 m. Let us assume that his initial velocity was zero and neglect the effect of the air on the ball during the fall. (a) How long did Munday fall to reach the water surface below the falls? …