# 2.4 Acceleration  (Page 2/8)

 Page 2 / 8

## Calculating acceleration: a racehorse leaves the gate

A racehorse coming out of the gate accelerates from rest to a velocity of 15.0 m/s due west in 1.80 s. What is its average acceleration?

Strategy

First we draw a sketch and assign a coordinate system to the problem. This is a simple problem, but it always helps to visualize it. Notice that we assign east as positive and west as negative. Thus, in this case, we have negative velocity.

We can solve this problem by identifying $\Delta v$ and $\Delta t$ from the given information and then calculating the average acceleration directly from the equation $\stackrel{-}{a}=\frac{\Delta v}{\Delta t}=\frac{{v}_{f}-{v}_{0}}{{t}_{f}-{t}_{0}}$ .

Solution

1. Identify the knowns. ${v}_{0}=0$ , ${v}_{f}=-\text{15}\text{.0 m/s}$ (the negative sign indicates direction toward the west), $\Delta t=1\text{.80 s}$ .

2. Find the change in velocity. Since the horse is going from zero to $-\text{15.0 m/s}$ , its change in velocity equals its final velocity: $\Delta v={v}_{f}=-\text{15}\text{.0 m/s}$ .

3. Plug in the known values ( $\Delta v$ and $\Delta t$ ) and solve for the unknown $\stackrel{-}{a}$ .

$\stackrel{-}{a}=\frac{\Delta v}{\Delta t}=\phantom{\rule{0.15em}{0ex}}\frac{-\text{15}\text{.0 m/s}}{1\text{.80 s}}=-8\text{.33 m}{\text{/s}}^{2}.$

Discussion

The negative sign for acceleration indicates that acceleration is toward the west. An acceleration of $8\text{.33 m}{\text{/s}}^{2}$ due west means that the horse increases its velocity by 8.33 m/s due west each second, that is, 8.33 meters per second per second, which we write as $8\text{.33 m}{\text{/s}}^{2}$ . This is truly an average acceleration, because the ride is not smooth. We shall see later that an acceleration of this magnitude would require the rider to hang on with a force nearly equal to his weight.

## Instantaneous acceleration

Instantaneous acceleration $a$ , or the acceleration at a specific instant in time , is obtained by the same process as discussed for instantaneous velocity in Time, Velocity, and Speed —that is, by considering an infinitesimally small interval of time. How do we find instantaneous acceleration using only algebra? The answer is that we choose an average acceleration that is representative of the motion. [link] shows graphs of instantaneous acceleration versus time for two very different motions. In [link] (a), the acceleration varies slightly and the average over the entire interval is nearly the same as the instantaneous acceleration at any time. In this case, we should treat this motion as if it had a constant acceleration equal to the average (in this case about $1\text{.}8 m{\text{/s}}^{2}$ ). In [link] (b), the acceleration varies drastically over time. In such situations it is best to consider smaller time intervals and choose an average acceleration for each. For example, we could consider motion over the time intervals from 0 to 1.0 s and from 1.0 to 3.0 s as separate motions with accelerations of $+3\text{.}0 m{\text{/s}}^{2}$ and $\text{–2}\text{.}0 m{\text{/s}}^{2}$ , respectively.

#### Questions & Answers

Calculate the work done by an 85.0-kg man who pushes a crate 4.00 m up along a ramp that makes an angle of 20.0º20.0º with the horizontal. (See [link] .) He exerts a force of 500 N on the crate parallel to the ramp and moves at a constant speed. Be certain to include the work he does on the crate an
Collins Reply
What is thermal heat all about
Abel Reply
why uniform circular motion is called a periodic motion?.
Boniface Reply
when a train start from A & it returns at same station A . what is its acceleration?
Mwdan Reply
what is distance of A to B of the stations and what is the time taken to reach B from A
BELLO
the information provided is not enough
aliyu
Hmmmm maybe the question is logical
yusuf
where are the parameters for calculation
HENRY
there is enough information to calculate an AVERAGE acceleration
Kwok
mistake, there is enough information to calculate an average velocity
Kwok
~\
Abel
what is the unit of momentum
Abel
wha are the types of radioactivity ?
Worku Reply
what are the types of radioactivity
Worku
what is static friction
Golu Reply
It is the opposite of kinetic friction
Mark
static fiction is friction between two surfaces in contact an none of sliding over on another, while Kinetic friction is friction between sliding surfaces in contact.
MINDERIUM
I don't get it,if it's static then there will be no friction.
author
It means that static friction is that friction that most be overcome before a body can move
kingsley
static friction is a force that keeps an object from moving, and it's the opposite of kinetic friction.
author
It is a force a body must overcome in order for the body to move.
Eboh
If a particle accelerator explodes what happens
Eboh
why we see the edge effect in case of the field lines of capacitor?
Arnab
what is wave
Muhammed Reply
what is force
Muhammed
force is something which is responsible for the object to change its position
MINDERIUM
more technically it is the product of mass of an object and Acceleration produced in it
MINDERIUM
wave is disturbance in any medium
iqra
energy is distributed in any medium through particles of medium.
iqra
If a particle accelerator explodes what happens
Eboh Reply
we have to first figure out .... wats a particle accelerator first
Teh
What is surface tension
Subi Reply
The resistive force of surface.
iqra
Who can tutor me on simple harmonic motion
yusuf Reply
on both a string and peldulum?
Anya
spring*
Anya
Yea
yusuf
Do you have a chit-chat contact
yusuf
I dont have social media but i do have an email?
Anya
Which is
yusuf
Where are you chatting from
yusuf
I don't understand the basics of this group
Jimmy
teach him SHM init
Anya
Simple harmonic motion
yusuf
how.an.equipotential.line is two dimension and equipotential surface is three dimension ?
syed Reply
definition of mass of conversion
umezurike Reply
Force equals mass time acceleration. Weight is a force and it can replace force in the equation. The acceleration would be gravity, which is an acceleration. To change from weight to mass divide by gravity (9.8 m/s^2).
Marisa
how many subject is in physics
Adeshina Reply
the write question should be " How many Topics are in O- Level Physics, or other branches of physics.
effiom
how many topic are in physics
Praise
Praise what level are you
yusuf
If u are doing a levels in your first year you do AS topics therefore you do 5 big topic i.e particles radiation, waves and optics, mechanics,materials, electricity. After that you do A level topics like Specific Harmonic motion circular motion astrophysics depends really
Anya
Yeah basics of physics prin8
yusuf
Heat nd Co for a level
yusuf
yh I need someone to explain something im tryna solve . I'll send the question if u down for it
Tamdy Reply
a ripple tank experiment a vibrating plane is used to generate wrinkles in the water .if the distance between two successive point is 3.5cm and the wave travel a distance of 31.5cm find the frequency of the vibration
Tamdy
hallow
Boniface
please send the answer
Boniface
the range of objects and phenomena studied in physics is
Bethel Reply
I don't know please give the answer
Boniface

### Read also:

#### Get the best College physics course in your pocket!

Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics' conversation and receive update notifications?

 By By By