Acceleration

Changes in Velocity

Acceleration Changing Velocity

There are two major indicators that the velocity of an object has changed over time

Change in spacing of dots

Differences in lengths of velocity vectors

If object speeds up, subsequent velocity vector longer If object slows down, each vector shorter than previous one

Acceleration Acceleration

Acceleration - Rate at which object’s velocity changes

When velocity of object changes at constant rate, has constant acceleration

Acceleration Velocity-Time Graphs

Acceleration Average and Instantaneous Acceleration

Average acceleration - Change in velocity during measurable time interval divided by time interval

Instantaneous acceleration - Change in velocity at instant of time

Measured in m/s2

Acceleration Average and Instantaneous Acceleration

Instantaneous acceleration found by drawing tangent line on velocity-time graph at point of time in which interested. Slope of line equal to instantaneous acceleration

Acceleration Velocity and Acceleration

How would you describe the sprinter’s velocity and acceleration as shown on the graph?

Sprinter’s velocity starts at zero, increases rapidly for first few seconds, then, after reaching about 10.0 m/s, remains almost constant

Acceleration Positive and Negative Acceleration

First - positive direction speeding up

Second - positive direction slowing down

Third speeding up negative direction

Fourth slowing down negative direction

Acceleration Positive and Negative Acceleration

When speeding up, velocity and acceleration vectors

point in same direction

When slowing down, acceleration and

velocity vectors point in opposite direction

Both direction of velocity and acceleration needed to

determine whether speeding up or slowing down

Positive acceleration when acceleration vector points in

positive direction, and negative when vector points in

negative direction

Sign does not indicate whether object speeding up or slowing down

Acceleration Determining Acceleration from v-t Graph

Assume positive direction east

If no slope, acceleration zero

A and E constant velocity

B - positive velocity and constant,

positive acceleration

C negative slope, motion slows down,

and stops (acceleration and velocity opposite)

C and B crossing point shows velocities equal. Does not give runners’ positions

Acceleration Determining Acceleration from v-t Graph

D - starts toward west, slows down, for instant zero velocity, then moves east increasing speed. Slope positive. Velocity and acceleration in opposite directions, speed decreases and equals zero at time graph crosses the axis. After that time, velocity and acceleration in same direction and speed increases

Acceleration Determining Acceleration from v-t Graph

Average acceleration expressed as slope of velocity-time graph

Acceleration Determining Acceleration from v-t Graph

On the basis of the velocity-time graph of a car moving up a hill, determine the average acceleration of the car?

Velocity with Average Acceleration

Average acceleration:

Rewritten as follows:

And rearranged again:

Motion with Constant Acceleration

Motion with Constant Acceleration Velocity with Average Acceleration

When acceleration constant; average acceleration, ā, is the same as instantaneous acceleration, a

Equation for final velocity can be rewritten to find time at which object with constant acceleration has given velocity

Also used to calculate initial velocity when both velocity and time given

Motion with Constant Acceleration Position with Constant Acceleration

Graph shows motion not uniform:

Displacements get larger

Slope of constant acceleration gets steeper

Motion with Constant Acceleration Position with Constant Acceleration

Slopes used to create velocity-time graph contains information about displacement

v - height of plotted line above t-axis

Δt - width of shaded rectangle

Area of rectangle is vΔt,

or Δd (displacement)

Motion with Constant Acceleration Position with Constant Acceleration

Graph shows the motion of an airplane. Find the displacement of airplane at Δt = 1.0 s and at Δt = 2.0 s

Motion with Constant Acceleration An Alternative Expression

Often, it is useful to relate position, velocity, and constant acceleration without including time

Pg. 68

Motion with Constant Acceleration An Alternative Expression

Rearrange vf = vi + ātf, to solve for time:

Rewriting di = df + vitf + ātf2

12

Motion with Constant Acceleration An Alternative Expression

From the graph as shown, if a car slowing down with a constant acceleration from initial velocity vi to the final velocity vf, write the equation for the total distance (Δd) traveled by the car

Motion with Constant Acceleration An Alternative Expression

On the v-t graph shown on the right, for an object moving with constant acceleration that started with an initial velocity of vi, derive the object’s displacement

Free Fall Acceleration due to gravity concept in motion

At the top of its flight, the ball’s velocity is 0 m/s. What would happen if its acceleration were also zero?

The ball’s velocity would remain at 0 m/s

It would simply hover in the air at the top of its flight

Acceleration of an object at the top of its flight can’t be zero. Further, acceleration must be downward

Free Fall Acceleration Due to Gravity

Amusement parks use the concept of free fall to design rides that give the riders the sensation of free fall

Rides usually consist of three parts: the ride to the top, momentary suspension, and the plunge downward

When the cars are in free fall, the most massive rider and the least massive rider will have the same acceleration

Free Fall What is Free Fall?

Free fall is the motion of the body when air resistance is negligible and the action can be considered due to gravity alone

Gravity = 9.8 m/s2

Acceleration Due to Gravity

Suppose the free-fall ride at an amusement park starts at rest and is in free fall for 1.5 s. What would be its velocity at the end of 1.5 s?

Free Fall

Acceleration Due to Gravity

How far does the ride fall? (Hint: Use the equation for displacement when time and constant acceleration are known)

Free Fall