Applications of Calculus (1 Viewer)

[jkerr138]

A particle is moving along the x-axis. Its displacement x metres from the origin after t seconds, is given by x= e^t - 2e^2t for 0 is less than equal to t or t is less than or equal to 2 (greater than or less than equal to)

i) Find the initial velocity of the particle
ii) Explain why the particle never comes to rest
iii) Find the distance travelled by the particle between t=0 and t=2 seconds.

Part i) I'm fine with, but I don't know how to explain why the particle won't come to rest. I graphed it and it appears the roots are outside of the domain. What is an acceptable form of response for ii)
Thanks.

 

[InteGrand]

A particle is moving along the x-axis. Its displacement x metres from the origin after t seconds, is given by x= e^t - 2e^2t got 0<t<2 (greater than or less than equal to)

i) Find the initial velocity of the particle
ii) Explain why the particle never comes to rest
iii) Find the distance travelled by the particle between t=0 and t=2 seconds.

Part i) I'm fine with, but I don't know how to explain why the particle won't come to rest. I graphed it and it appears the roots are outside of the domain. What is an acceptable form of response for ii)
Thanks.

Here's a graph of the velocity (on the vertical axis) against time (horizontal axis): http://www.graphsketch.com/?eqn1_co..._lines=1&line_width=4&image_w=850&image_h=525

 

[jkerr138]

Another question.

An object is moving along the x-axis. The graph shows the velocity, v ms^-1 of the object as a function of time, t seconds.
The coordinates of the points shown on the graph are A (3,27), B (6,36), C (9,0) and D (11,-24). The object is initially at x= 3 and the velocity is constant for t is greater than or equal to 11.

i) Use Simpsons Rule with three (3) function values to approximate the distance travelled by the object between t=0 and t=6.
ii) Approximately when will the object pass through the origin?

If I have done my 3 function value inputs correctly, I have t=0, t= 2, t=4 and t=6 , but I don't have any values for t=2 or t=4. Not sure what to do?

 

[InteGrand]

Another question.

An object is moving along the x-axis. The graph shows the velocity, v ms^-1 of the object as a function of time, t seconds.
The coordinates of the points shown on the graph are A (3,27), B (6,36), C (9,0) and D (11,-24). The object is initially at x= 3 and the velocity is constant for t is greater than or equal to 11.

i) Use Simpsons Rule with three (3) function values to approximate the distance travelled by the object between t=0 and t=6.
ii) Approximately when will the object pass through the origin?

If I have done my 3 function value inputs correctly, I have t=0, t= 2, t=4 and t=6 , but I don't have any values for t=2 or t=4. Not sure what to do?

Do you have a value for t = 0? The values you need are values at t = 0, 3, 6. The values for t = 3 and t = 6 are given.

 

[jkerr138]

Wouldn't it be x=3 as the question says it is initially at x=3 ?

 

[InteGrand]

Wouldn't it be x=3 as the question says it is initially at x=3 ?

No, that's the initial position, not velocity.

 

[jkerr138]

Ah right. Then I'm not sure then.