# PhysicsMotion in straight line

#### Shah 72

##### Active member
A particle moves on a straight line. It starts at a point O on the line and returns to O 100 s later. The velocity of P is v m/s at time t s after leaving O where v= 0.000t^3- 0.015t^2 +0.5t.
1) Find the values of v at the times for which the acceleration of P is zero
I got when t= 21.1s, V= 4.81m/s and when t= 78.9s v= -4.81m/s
2) sketch the velocity time graph for Ps motion for 0<t<100
So I plotted for t=0 v=0, t= 21.1 v=4.81, t= 78.9, v= -4.81 and t=100, v=0. So it will be two curves with the curve going up between 0 and 50 and curve going down between 50 and 100.
Is this right??
3) Find the greatest distance of P from 0 for 0<t<100
I don't understand this part.

#### topsquark

##### Well-known member
MHB Math Helper
A particle moves on a straight line. It starts at a point O on the line and returns to O 100 s later. The velocity of P is v m/s at time t s after leaving O where v= 0.000t^3- 0.015t^2 +0.5t.
1) Find the values of v at the times for which the acceleration of P is zero
I got when t= 21.1s, V= 4.81m/s and when t= 78.9s v= -4.81m/s
2) sketch the velocity time graph for Ps motion for 0<t<100
So I plotted for t=0 v=0, t= 21.1 v=4.81, t= 78.9, v= -4.81 and t=100, v=0. So it will be two curves with the curve going up between 0 and 50 and curve going down between 50 and 100.
Is this right??
3) Find the greatest distance of P from 0 for 0<t<100
I don't understand this part.
Your problem statement has a typo. I used your answer to 1) to get that $$\displaystyle v = 0.003t^3 - 0.015t^2 + 0.5t$$

Call s(t) the distance function and define s(O) = 0. What is the greatest value of s for 0 < t < 100?

-Dan

• Shah 72

#### Shah 72

##### Active member
Your problem statement has a typo. I used your answer to 1) to get that $$\displaystyle v = 0.003t^3 - 0.015t^2 + 0.5t$$

Call s(t) the distance function and define s(O) = 0. What is the greatest value of s for 0 < t < 100?

-Dan
So the greatest distance is when t=50s which is 156.25m.

#### Shah 72

##### Active member
Your problem statement has a typo. I used your answer to 1) to get that $$\displaystyle v = 0.003t^3 - 0.015t^2 + 0.5t$$

Call s(t) the distance function and define s(O) = 0. What is the greatest value of s for 0 < t < 100?

-Dan
Thanks very much!

#### skeeter

##### Well-known member
MHB Math Helper
It starts at a point O on the line and returns to O 100 s later.
Your problem statement has a typo. I used your answer to 1) to get that $$\displaystyle v = 0.003t^3 - 0.015t^2 + 0.5t$$
$v(t) \ge 0$ for all $t \ge 0$ ... this says the particle always moves in the positive direction away from the starting point O.

• Shah 72

#### Shah 72

##### Active member
$v(t) \ge 0$ for all $t \ge 0$ ... this says the particle always moves in the positive direction away from the starting point O.

No the question says that it moves in a straight line. It starts at point O and returns to point O 100s later

#### skeeter

##### Well-known member
MHB Math Helper
No the question says that it moves in a straight line. It starts at point O and returns to point O 100s later
Velocity is a vector quantity ... if v(t) > 0 for all t > 0, then the particle moves in the positive direction only. To return to its starting position, it must have a negative velocity.

Check the given velocity function again ... the one you posted will not work.

#### Shah 72

##### Active member
Velocity is a vector quantity ... if v(t) > 0 for all t > 0, then the particle moves in the positive direction only. To return to its starting position, it must have a negative velocity.

Check the given velocity function again ... the one you posted will not work.
Yeah I agree you are right. The velocity between 50 to 100 is negative so it comes back. I wasn't understanding the last question which asked for the greatest distance in the given time interval between 0 and 100. Since there are more time intervals in between which is 21.1 s where the velocity is positive and 78.9s where the velocity is negative, I was thinking whether I should take these intervals too when I calculate the greatest distance

#### skeeter

##### Well-known member
MHB Math Helper
• topsquark

#### Shah 72

##### Active member
Once again, is the velocity function $v(t) = 0.003t^3 - 0.5t^2 + 0.5t$ ?

If so, look at the graph of velocity … if not, post the correct velocity function.

View attachment 11336
V=0.0001t^3-0.015t^2+0.5t

• topsquark

#### skeeter

##### Well-known member
MHB Math Helper
• Shah 72