MOTION – Part 2

Acceleration

PhysicsCh. 4

Acceleration is the rate of change of velocity in a specific direction.

It is a VECTOR quantity – has magnitude & direction.

Any change in the velocity (either in magnitude or direction) is acceleration.

What is Acceleration?

1. Which car or cars (red, green, and/or blue) are undergoing an acceleration?

Study each car individually in order to determine the answer.

2. Which car (red, green, or blue) experiences the greatest acceleration?

An object’s motion is determined by a combination of velocity & acceleration.

We have to look at the magnitude and direction of each.

Objects that are in acceleration MUST have a changing velocity.

Objects in Motion

Constant Acceleration

Changing Acceleration

Velocity must be changing by a constant amount.

In the table above, the velocity changes by 4 each second.

Velocity is changing at each second.

This table shows no consistency in the velocity, but it does show an increase in velocity over time.

Units for acceleration are m/s2. Sometimes this is written as m/s/s.

Calculating Average Acceleration

Example A:

Example B:

POSITIVE Acceleration

Example C:

Example D:

NEGATIVE Acceleration

1. As a shuttle bus comes to a normal stop. It slows from 9.0 m/s to 0.0 m/s in 5.0 s. Find the average acceleration of the bus.

2. Find the acceleration of an amusement park ride that starts from rest to a speed of 28 m/s in 3.0s.

3. A car traveling west on Plymouth Road initially starts at 8.0 m/s and accelerated 2.5 m/s2 for 3.0 s. What is the final velocity of the car?

4. Find the time required for a dump truck with an average acceleration of 0.80 m/s2 to reach 27 m/s from rest.

Example Problems

We can use a V-T graph to determine an object’s acceleration.

Constant Velocity = ZERO Acceleration

+ Velocity = + Acceleration

Velocity – Time Graphs

POSITIVE Velocity NEGATIVE Velocity

Using a Graph to Determine Motion

SPEEDING UP SLOWING DOWN

The MAGNITUDE of velocity is INCREASING.

The line on the graph is going further away from the x-axis.

+3 m/s to +9 m/s

-3 m/s to -9 m/s

The MAGNITUDE of the velocity DECREASING.

The line on the graph is approaching the x-axis.

+9 m/s to +3 m/s

-9 m/s to -3 m/s

POSITIVE Velocity& POSITIVE Acceleration

POSITIVE Velocity& NEGATIVE Acceleration

NEGATIVE Velocity& NEGATIVE Acceleration

NEGATIVE Velocity & POSITIVE Acceleration

MOTION VELOCITY ACCELERATION

Speeding UP + +

Speeding UP - -

Slowing DOWN + -

Slowing DOWN - +

Constant Velocity - or + 0

Speeding UP from REST

0 - or +

Remaining at REST 0 0

Speeding Up or Slowing Down?

REST

Constant Velocity

Speeding Up

Slowing Down

Strobe Pictures / Motion DiagramsDetermine the motion of the following balls:

Describe the position, velocity, and acceleration shown by each motion diagram.(1second intervals)

● ● ● ● ●0m 1m 2m 3m 4m

● ● ● ● ● ● 0m .2m .6m 1.4m 2.4m 3.6m

● ● ● ● ● ● 0m 1.6m 2.4m 2.8m 3.0m 3.1m

● ● ● ● ● 0m .5m 1.0m 1.5m 2.0m

Motion Diagrams

1. Is the motion of the ball moving with a constant velocity or accelerating?

• Accelerating

2. Is the acceleration of the ball positive, negative, or zero?

• Positive (the velocity is increasing)

3. Estimate the velocity of the ball at a) 5 cm b) 20 cmc) 44 cmd) 79 cm

4. What is the average acceleration of the ball?

Ball rolling to the right. (strobe flash every

0.5s)

There are 5 variables we are interested in now. Δx , Vf , Vi , a, and t

These are 4 equations which are used to calculate/solve a wide variety of problems.

We will focus on these as we study free fall next.

Notice that each equation has 4 variables and one missing.

Kinematic Equations

Equation Missing

x

tvvx f 02

1avga

20 2

1tatvx avg fv

xavv avgf 220

2 t

tavv avgf 0

4.3 Free Fall and the Acceleration due to Gravity

An object is in free fall if it is moving under the sole influence of gravity.

Free-falling objects speed up, or accelerate, as they fall.

The acceleration of -9.8 m/s2 is given its own name and symbol—acceleration due to gravity (g).

4.3 Free fall with initial velocity

The motion of an object in free fall is described by the equations for speed and position with constant acceleration.

The acceleration (a) is replaced by the acceleration due to gravity (g) and the variable (x) is replaced by (y).

-

+

-

+

4.3 Free fall with initial velocity When the initial speed is

upward, at first the acceleration due to gravity causes the speed to decrease.

After reaching the highest point, its speed increases exactly as if it were dropped from the highest point with zero initial speed.

4.3 Solving problems with free fall

Most free-fall problems ask you to find either the height or the speed.

Height problems often make use of the knowledge that the speed becomes zero at the highest point of an object’s motion.

If a problem asks for the time of flight, remember that an object takes the same time going up as it takes coming down.

1. You are asked for distance.2. You are given an initial speed and time of flight.3. Use v = v0 + gt and y = y0 + v0t + ½ gt2

4. Since y0 and v0 = 0, the equation reduces to y = ½ gt2

◦ y = (0.5) (-9.8 m/s2) (1.6s)2

◦ y = -12.5 m (The negative sign indicates the height is lower than the initial height)

Calculating height from the time of falling

A stone is dropped down a well and it takes 1.6 seconds to reach the bottom. How deep is the well? You may assume the initial speed of the stone is zero.

4.3 Air Resistance and Mass

The acceleration due to gravity does not depend on the mass of the object which is falling.

Air creates friction that resists the motion of objects moving through it.

All of the formulas and examples discussed in this section assume a vacuum (no air).

4.3 Terminal Speed You may safely assume that a = g = -9.8

m/sec2 for speeds up to several meters per second.

The air resistance from friction increases as a falling object’s speed increases.

Eventually, the rate of acceleration is reduced to zero and the object falls with constant speed.

The maximum speed at which an object falls when limited by air friction is called the terminal velocity.