Question

For 0≤ t ≤6, a particle is moving along the x-axis. The particle’s position, x(t ), is not explicitly given.
The velocity of the particle is given by v(t) = 2sin(e^(t/4 )) + 1. The acceleration of the particle is given by (1/2 ) e ^(t/4)cos(e^(t/4)
and x(0) =2.

Answer 1

where is the answer for this question?

Answer 2

How can I determine if the speed is increasing or decreasing at time 5.5

Answer 3

To detemine if the speed is increasing or decreasing at a certain point in time, evaluate the acceleration at that time.

Answer 4

How can I find the average velocity of the particle between 0<t<6?

Answer 5

well the answer I got was to evaluate v(5.5) and a(5.5) and since they both have negative value, the speed is increasing. I dont understand that because I cant visualize it

Answer 6

Thomas9, you said to evaluate using only accelleration? But why?

Answer 7

You're right, you should evaluate the speed too. I wasn't considering negative speed.

Answer 8

This is for my calculus class

Answer 9

velocity is not the same as speed; velocity is both a direction and a value, while speed is only a value with no direction

Answer 10

I remember that speed is suppose to be the absolute value of velocity, is that right?

Answer 11

I wasn't considering negative velocity in that case.

Answer 12

But I still am a little confused, how does velocity and acceleration having the same sign, make it that the speed of the particle is increasing

Answer 13

Anyway if velocity and accelaration have the same sign, then speed is increasing, if the have opposite sign, then speed is decreasing.

Answer 14

because with acceleration, it doesn't matter if you're moving one direction or the other, you're still accelerating or deccelerating whether you're going one direction or the other

Answer 15

Ok. I get it now. So it doesnt matter what the sign is as along as they have the same sign, speed is increasing? and different sign, speed is decreasing? How does that relate calculus?
Does it have to do with tangent lines?

Answer 16

I don't see a direct link with tangent lines, or calculus for that matter.

Answer 17

I got this question from a calculus textbook and therefore I am relating it to calculus

Answer 18

I think the next question about the average is more of a calculus question.

Answer 19

I also asked another question..Yes that is the question I want to ask next, average velocity

Answer 20

What exactly are we finding if we are asked to find average velocity between o<t<6? The average speed you are going from time 0 to 6?

Answer 21

By definition of the average of a function, you need to integrate the velocity between the boundaries 0 and 6, and divide by 6.

Answer 22

yeah, tho, speed is pretty much the absolute value of velocity
that part of the problem mostly comes from definitions in physics. i think khanacademy made a video on that exact problem at one point but also made the same mistake concerning velocity/speed.... :P

Answer 23

of course the integral over velocity is the accellaration.

Answer 24

ok I get that part, by why divide by 6? because you are subtracting from 0 to 6?

Answer 25

Just following the formula: http://en.wikipedia.org/wiki/Average#Averages_of_functions

Answer 26

Ok thank you very much Thomas9 and accessdenied

Answer 27

the integral of your velocity is the distance, and the average velocity is distance/time on that interval
in case that helps understand whats going on

Answer 28

Of course, my bad.