According to , three cars P, Q and R are at three points along the x-axis at a given moment. Now the car p starts its motion towards P_(1) parallel to the y-axis with a uniform velocity v. Again, R is in motion paraIIeI to the y-axis along "RR"_(1) with uniform acceleration a. If the car Q too moves paraIIeI to the y-axis then under what condition will aII of them remain coIIinear? Given PQ = QR.

According to , three cars P, Q and R are at three points along the x-a

1.	According to , three cars P, Q and R are at three points along the x-axis at a given moment. Now the car p starts its motion towards P_(1) parallel to the y-axis with a uniform velocity v. Again, R is in motion paraIIeI to the y-axis along "RR"_(1) with uniform acceleration a. If the car Q too moves paraIIeI to the y-axis then under what condition will aII of them remain coIIinear? Given PQ = QR.
Answer» <P> Solution :LET the time be t after which P and R are at `P_(1)` and `R_(1)` respectively. `:. ""PP_(1) = vt " ""and" " ""RR"_(1) = (1)/(2)at^(2)` According to the question after time t, Q will be at `Q_(1)`. From the figure we have , `(PP_(1))/(PM) = ("QQ"_(1))/(QM)=("RR"_(1))/(RM)=k` (say) `:. "" PP_(1)= k.PM = k(PQ+QM)` `"QQ"_(1) = k.QM` and `"RR"_(1)=k.RM = k(QR-QM)` `:."""PP"_(1)-"RR"_(1)=k.(QM+QM)" "[becausePQ=QR]` = 2 k.QM `:.""k.QM= ("PP"_(1)-"RR"_(1))/(2)` `:. """QQ"_(1) = k.QM` `=("PP"_(1)-"RR"_(1))/(2)=(PP_(1))/(2)-("RR"_(1))/(2)=(vt)/(2)-(1)/(4)at^(2)` `:."" "QQ"_(1)=((v)/(2))t-(1)/(2)((a)/(2)).t^(2)` Comparing equation (1) with s = ut `-(1)/(2)at^(2)` , we can say that to remain in the same straight line joining the other two cars, the initial velocity of the car Q must b `(v)/(2)` along the positivey-axis and it should move with a retardation `(a)/(2)`.