IIT JEE , AIEEE Forum - Physics , Mechanics

luxmi

in this question there will be two values of time, bcos of a quadratic equation, wat does it mean?

a particle starts with velocity of 200cm/s and moves in a straight line with a retardation of 10cm/s²,find the time it takes to describe 1500cm.

karthik2007

Use S = ut + 0.5at²

here, S = 1500, u = 200, a = -10.

Now you will get a quadratic equation in t, hence two values of time... reject the negative value

luxmi

but both values r positive

Raghudevan

we know V(i) = 200cm/sec, a = 10cm/sec and s = 1500cm

also, s = V(i)t + (1/2)a(t^2)

so we get,

1500 = 200t + 5(t^2)

(t^2) + 40t - 300 = 0

t = [-40

^{[2 ]}

1600 + 1200]2

t = [-20

10^{[2 ]}

7]

t = 6.45sec

here we also get a negtive value for time which is meaninless, ie, it has no physical significance. so we reject it and accept the +ve value only.

i hope this solves ur query

luxmi

hey, this is retardation. so the equation is:

1500=200t-5t²

so t²-40t+300=0

svj29

ya so one root is coming positive and the odr negative..ur ansrs are 30secs and -10secs.....neglect the scnd one.....

crack

you will get two answers 10s and 30s .....here initial velocity=200cm/s and a=-10m/s ^2
a=v/ t
if we substitute the value for t as 10m/s we get the correct value and the other one doesn't match the acceleration value given...
hence chuck 30 s

Raghudevan

yeah, sorry (t^2) - 40t + 300 = 0

t = [40

^{[2 ]}

1600 - 1200]/2

t = [20

10]

t = 30 sec or 10 sec

we know that the body is under const deceleration of 10cm/sec, so in the first 10 sec itself, the body would have covered 1500cm in the positive direction, then it'll come to a stop, then due to the acc in the -ve direction, it'll start moving in the -ve direction with const acc of 10cm/sec, it takes the body 30sec to cover 1500cm in the -ve direction, first it would have covered 1500cm in the +ve direction, then stopped and then started moving in the -ve direction, it would have covered 1500cm again to reach the mean position and then moved onto 1500cm in the -ve direction, the total time taken for this is 30sec, the net displacement is -1500cm, if we sub, v = 200cm/sec, a = -10cm/sec^2 and t = 30 sec, we get this

crack

dude iam not sure whether you are right...but as far as i know negative acceleration doesn't mean that it goes in the negative direction

Raghudevan

-ve const acc means that there is some force that acts in the -ve direction on the body. this force will cause the body to first stop and then move on in the -ve direction. but the force has to be const, if the force is const , then the acc is also const(unless of coure we dont consider a variable mass system) :)

rooney

As the body slows down, it will cross 1500 cm distance at time=10 sec, stop after some distance, start to come back towards where it started from and cross the same location (which is at 1500cm from starting point) at time=30 sec but with velocity in the opposite direction.

luxmi

but in da question it is give that it is retardation. does it mean that retardation and negative acceleration are same???

rooney

Yes they are same.

Raghudevan

yeah, retardation just means acc in the -ve direction, this is caused by some force, as the retardation is const, that force is too, so after it stops the body it will acc the body in the -ve direction

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