Why is the -0.5 term irrelevant in solving equations of motion?

[Andy21]

Homework Statement

An air track glider is placed on a linear air-track which is slightly tilted. It is given a velocity of 1.5 metres per second up the track. If its acceleration is 2 metres per second squared down the track, find the time at which it is 1m below its starting point.

Please explain how to solve this problem. Thanks

Homework Equations

The Attempt at a Solution

s=(u+v)/2 xt


1= (1.5+v)/2 x t

t=1-(1.5+v)/2

 

[jmb88korean]

try using the equation final position= initial position + (initial velocity)(time) +1/2(acceleration)(time)^2. also try making the final position negative because it is below the starting point

 

[Andy21]

Thanks for the help. I have got to t+1/t=1.5
Can you help me from here to find t.

 

[jmb88korean]

if i did the problem, it would become -1m= 0m + 1.5t + (1/2)2t^2. by moving the -1 over to the other side, i would use the quadratic formula dueto the equation becoming, t^2 +1.5t+1. (i just re-arranged it after moving the one over.

 

[Andy21]

I have tried to use the quadratic formula but there is a negative discriminant so so it won't work. Are there other ways to solve the equation?

 

[jmb88korean]

i see. the acceleration is negative. i did not see that. so the equation should be -(t)^2 +1.5t +1 . quadratic should give you two answers, one of which should work.

 

[Ambidext]

I have tried to use the quadratic formula but there is a negative discriminant so so it won't work. Are there other ways to solve the equation?

Hi, if my understanding towards your question is correct, that the initial velocity of the glider is 1.5 m s^-1 upwards, acceleration is 2 ms^-2 downwards, and that you need to find the time at which displacement is 1m downwards,

then I'll be using the same method as jmb88korean:

s = ut + 0.5at²

1 = 1.5t + 0.5(2)t²
t² - 1.5t -1 = 0
t = ( -(-)1.5 +/- root(1.5² + 4)) / 2
t = 2 or -0.5

Since by convention, there is no such thing is negative t, we take t = 2.

 

[jmb88korean]

I calculated the same answers as Ambidext when I did the problem.

 

[Andy21]

Thankyou jmb88korean and Ambidext for the help, I agree that t=2 is the answer.

 

[Ambidext]

Actually, mathematically, we know how to omit -0.5.

Can anyone explain though, why, in Newtonian mechanics concept, WHY the -0.5 is irrelevant?