If the speedometer of a car reads a constant 40km/hr, can you say the car has a constant velocity? Why or why not?

- calculusxy

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- calculusxy

@Michele_Laino This is like basic physics.

- alekos

velocity is defined as speed and direction

- Michele_Laino

I think that we can only say that the magnitude of our velocity is 40 Km/h

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## More answers

- Michele_Laino

namely, the motion of our car can be a uniform circular motion

- calculusxy

So is it a yes?

- Michele_Laino

I think no, since as @alekos as well said the velocity is a vector quantity, which is defined by a speed or magnitude and a direction

- calculusxy

So since it doesn't have a specific direction it cannot be considered as a "constant velocity," even though it has a constant speed?

- Michele_Laino

yes! That's right!

- calculusxy

I have more questions, since I like to make sure many things. :)

- Michele_Laino

ok!

- calculusxy

What two controls in a car can use a change in speed?

- calculusxy

I wrote the gas and brake pedals. But I am not sure if I should include the steering wheel, since it might change the velocity as well.

- Michele_Laino

I think that you have to include the steering wheel, since by means of the steering wheel we can bend the trajectory of our car, so we can change the velocity of our car

- calculusxy

So do i write the two pedals (gas and brake) and the steering wheel?

- Michele_Laino

yes! I think so!

- sweetburger

I agree that the steering wheel would cause a change in direction and therefore could have affect on the velocity

- calculusxy

Thanks for the continuous help. Next question: What quantity describes how quickly you change how fast you're traveling?

- sweetburger

Acceleration? right?

- calculusxy

Yes that's what I thought. But I am not quite sure.

- sweetburger

change in velocity over time*

- Michele_Laino

right! The steering wheel can produce a centripetal acceleration which is acting on our car @sweetburger

- calculusxy

@Michele_Laino For this question:What quantity describes how quickly you change how fast you're traveling? Would the answer be "acceleration"?

- alekos

Previously you asked
"What two controls in a car can change the speed?" (not velocity)
that would only be brake and gas pedal.

- Michele_Laino

yes! I think so, since the acceleration, as a number, is the change in speed

- sweetburger

@alekos I think you are correct considering it is only asking for change in speed.

- Michele_Laino

you are right! @alekos

- calculusxy

What is the acceleraiton of a car that travels in a straight line at a constant speed of 100km/hr?

- calculusxy

the acceleration would be 100km/hr since it is travels in a straight line

- sweetburger

if it is at a constant speed of 100km/hr there is no change in velocity so 0/t = 0

- Michele_Laino

if the speed is constant, then the acceleration as a simple number, and not as a vector quantity, is zero

- calculusxy

Oh okay

- sweetburger

the velocity must change over a specific period of time to find a acceleration value

- Michele_Laino

the acceleration as a vector quantity, since the motion is along a straight line, is the null vector

- calculusxy

What is the acceleration of a car moving along a straight line path that increases its speed from zero to 100km/hr in 10 seconds?

- calculusxy

Yes that's why i deleted it

- Michele_Laino

we have:
100 Km/h= 27.78 m/sec
so acceleration is:
27.78/10=2.778 m/sec^2

- calculusxy

yeah i was overlooking the "per hour" thank you for correcting that

- calculusxy

BY how much does the speed of a vehicle moving in a straight line change each second when it is accelerating at 2km/hr (two kilometers per hour per second; that is every second, the velocity is increasing two kilometers per hour.)

- Michele_Laino

after a time t (seconds), the requested change is
2*t Km/h

- calculusxy

I don't quite understand

- Michele_Laino

by definition, acceleration a is given by the subsequent formula:
\[a = \frac{{\Delta v}}{{\Delta t}}\]
so we have:
\[\Delta v = a\Delta t\]

- Michele_Laino

now, a= 2(Km/h)/sec
and if \Delta t= 1 seconds, then we can write:
\[\Delta v = a\Delta t = 2 \times 1 = 2\frac{{Km}}{h}\]

- anonymous

ansur at my fb :https://www.facebook.com/ParthKohli

- calculusxy

What does
\[a \Delta t\] mean

- calculusxy

@Michele_Laino

- calculusxy

Moving on to the next question:
Why does the unit of time never twice in the unit of acceleration?

- calculusxy

Would it be that the acceleration is found by dividing the velocity by time:
\[(distance / time) / time => distance / time^2\]

- Michele_Laino

\[a\Delta t\]
is the change in speed

- calculusxy

So how would i calculate the speed?

- calculusxy

QUestion: Calculate the speed (in m/s) of a skateboarder who accelerates from rest for 3 seconds down a ramp at an acceleration of 5/m^2.

- Michele_Laino

here we have to apply this formula:
\[v = a\Delta t = 5 \times 3 = ...m/\sec \]

- calculusxy

so for this question would we do:
\[V_f = V_i + (acceleration \times time)\]

- Michele_Laino

yes! nevertheless the initial speed is zero, since the skateboarder is starting from the rest

- calculusxy

V_i = 0 (initial velocity)
acceleration = 5 m / s^2
time = 3 seconds
\[V_f = 0 + (5 \times 3)\]

- Michele_Laino

that's right!

- calculusxy

15 m/s ?

- Michele_Laino

yes!

- calculusxy

THANK YOU SO MUCH!!! Last question:
Which has more acceleration when moving in straight line: car increasing its speed rom 50-60km/hr or a bicycle that goes from 0 to km/hr in the same time? Why?

- Michele_Laino

bycicle goes from 0 to ?

- calculusxy

10km/hr
Sorry

- Michele_Laino

if we consider a time interval \Delta t measured in hours, then the acceleration of the car is:
\[{a_{CAR}} = \frac{{\left( {60 - 50} \right)}}{{\Delta t}} = \frac{{10}}{{\Delta t}}\;\frac{{Km}}{{{h^2}}}\]
whereas the acceleration of the bycicle is:
\[{a_{BYCICLE}} = \frac{{\left( {10 - 0} \right)}}{{\Delta t}} = \frac{{10}}{{\Delta t}}\;\frac{{Km}}{h}\]

- Michele_Laino

oops..
\[{a_{BYCICLE}} = \frac{{\left( {10 - 0} \right)}}{{\Delta t}} = \frac{{10}}{{\Delta t}}\;\frac{{Km}}{{{h^2}}}\]

- calculusxy

So these are both the same right?

- Michele_Laino

sorry for my english:
bicycle*

- Michele_Laino

yes! They are the same

- calculusxy

Thanks!!!!!! I honestly love your help, you have been with me for the past hour!! OMG no one, believe me does that much, except for you!

- Michele_Laino

:)

- calculusxy

Sorry, but can you explain me the answer for the question: "BY how much does the speed of a vehicle moving in a straight line change each second when it is accelerating at 2km/hr (two kilometers per hour per second; that is every second, the velocity is increasing two kilometers per hour.) "

- calculusxy

I still didn't get it :(

- Michele_Laino

the speed change as function of time interval \Delta t, is given by the subsequent formula:
\[\Delta v = a\Delta t\]
where a is the acceleration

- Michele_Laino

in our case, we have:
\[a = 2\frac{{Km/h}}{{\sec }}\]

- Michele_Laino

so, if we consider a time interval \Delta t = 1 second, then after that time interval the speed change is:
\[\Delta v = a\Delta t = 2 \times 1 = 2\frac{{Km}}{h}\]
namely the requested speed change is:
2 Km/h

- calculusxy

So the answer itself is 2km/hr ?

- Michele_Laino

yes!

- calculusxy

Thank you! And for the question with the speed from 0 ti 100km/hr in 10 seconds
how did you get 27.78 m/sec

- Michele_Laino

since we have to divide by 3.6, namely
100/3.6 = 27.78 (approximated value)

- calculusxy

why 3.6?

- Michele_Laino

more explanation, we have:
\[1\frac{{Km}}{h} = \frac{{1000}}{{3600}}\frac{m}{{\sec }} = \frac{1}{{3.6}}\frac{m}{{\sec }}\]

- Michele_Laino

therefore:
\[1\frac{m}{{\sec }} = 3.6\frac{{Km}}{h}\]

- calculusxy

Oh okay!

- calculusxy

Thank you soo.... much!
May I know what times you are available in OS so that if i need help in physics/math, I can come and ask for your help?

- Michele_Laino

I'am available from 16:00 (Italy time zone)

- calculusxy

Well I am in NY so what would be the time in EST?

- Michele_Laino

I think 16-6= 9:00 am

- Michele_Laino

sorry:
16-6= 10:00 am

- calculusxy

oh okay so it's like 8pm in italy now?

- Michele_Laino

yes! at the moment it is 19:57 from me

- calculusxy

you use the military time a lot?

- calculusxy

or the 24 hour standard clock?

- Michele_Laino

I use the standard 24 hour clock

- calculusxy

okay b/c i use am and pm. anyway, thank you so much for your help. i REALLY appreciate it :)

- Michele_Laino

:)

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