Motion (Straight line) (2 Viewers)

[phyr3]

A particle P is moving along the x-axis. Its position at time t seconds is given by:

x= 2 sin t - t (t greater than/equal to 0)

Calculate the total distance travelled by the particle in the first PI seconds.


Also another question,

Whenever a train accelerates, it travels with a constant acceleration of 1ms^-2 and whenever it brakes, it decelerates at a constant retardation of 3ms^-2.
Find the time taken for a 1km journey on the train. Assume train starts from rest accelerates in a straight line and then immediately decelerates in straight line until at rest again.


Thanks in advance.

 

[Drongoski]

Is answer: 2sqrt(3) + pi/3 ??

 

[phyr3]

Is answer: 2sqrt(3) + pi/3 ??

YES T_T

howd you do it !!!

ahahah

 

[Drongoski]

YES T_T

howd you do it !!!

ahahah

Problem looks straightforward but it's easy to get it wrong.

v = dx/dt = 2cos t - 1 = 0 @ t = pi/3

From t=0 to t=pi/3: particle goes from x = 0 to x = 2*sqrt(3)/2 - pi/3 = sqrt(3) - pi/3

From t=pi/3 to pi, it reverses (changes direction) and goes to x = -pi (@ t=pi)

If you draw a simple diagram: you see total distance covered is :

sqrt(3) - pi/3 + (sqrt(3) - pi/3 + pi) = the answer.

You cannot just sub t=pi into x as that'd only give u the displacement (position)

 

[phyr3]

ahh get it now. thanks a lot.


Whenever a train accelerates, it travels with a constant acceleration of 1ms^-2 and whenever it brakes, it decelerates at a constant retardation of 3ms^-2.
Find the time taken for a 1km journey on the train. Assume train starts from rest accelerates in a straight line and then immediately decelerates in straight line until at rest again.

Anyone? =>

 

[eriito]

I got 9001

 

[Drongoski]

ahh get it now. thanks a lot.


Whenever a train accelerates, it travels with a constant acceleration of 1ms^-2 and whenever it brakes, it decelerates at a constant retardation of 3ms^-2.
Find the time taken for a 1km journey on the train. Assume train starts from rest accelerates in a straight line and then immediately decelerates in straight line until at rest again.

Anyone? =>

Is it 40sqrt(15)/3 secs ??

 

[phyr3]

nope >.<

10sqrt15

 

[Aerath]

I believe 10 sqrt 15 is only the acceleration movement. =\

 

[Drongoski]

I believe 10 sqrt 15 is only the acceleration movement. =\

According to my workings: acceleration phase = 10 sqrt(15) secs

Deceleration phase = 1/3 of acceleration phase

Therefore total journey takes 40 sqrt(15)/3 secs.

You can verify that: distance travelled during acceln = 1500/2 m and during deceleration = 1500/6 m

Where does this question come from; do u have its solution ?