141179 Two towns \(X\) and \(Y\) are connected by a regular bus service. \(A\) bus leaves in either direction at every \(t=T\) minutes. A man moving with some speed in the direction \(\mathrm{X}\) to \(\mathrm{Y}\) finds that a bus goes past him every \(t=t_{1}\) minutes in the direction of his motion, and every \(t=t_{2}\) minutes in the opposite direction. Then \(T\) is given by

141180 The co-ordinates \((x, y)\) of a moving particle at any time ' \(t\) ' are given by \(x=\alpha t^{3}\) and \(y=\beta t^{3}\). The speed of the particle at time ' \(t\) ' is given by

141181 Acceleration a is given in terms of position \(x\) as \(a=2 x \mathrm{~m} / \mathrm{s}^{2}\). At \(x=0\), the velocity \(v\) is zero. What is the relation between velocity \(v\) and position \(x\) ?

141182 Particle \(\mathbf{A}\) (which was located at the origin at time \(t=0\) ) is moving along the \(x\) - axis with a constant speed of \(1 \mathrm{~m} / \mathrm{s}\). Location of particle \(B\) which is moving along the \(\mathrm{Y}\) - axis is given by \(y\) \(=c t^{2}\), where \(c=1 \mathrm{~m} / \mathrm{s}^{2}\). Find the speed of particle \(A\) relative to particle \(B\) at \(t=1\) sec.

141179 Two towns \(X\) and \(Y\) are connected by a regular bus service. \(A\) bus leaves in either direction at every \(t=T\) minutes. A man moving with some speed in the direction \(\mathrm{X}\) to \(\mathrm{Y}\) finds that a bus goes past him every \(t=t_{1}\) minutes in the direction of his motion, and every \(t=t_{2}\) minutes in the opposite direction. Then \(T\) is given by

141180 The co-ordinates \((x, y)\) of a moving particle at any time ' \(t\) ' are given by \(x=\alpha t^{3}\) and \(y=\beta t^{3}\). The speed of the particle at time ' \(t\) ' is given by

141181 Acceleration a is given in terms of position \(x\) as \(a=2 x \mathrm{~m} / \mathrm{s}^{2}\). At \(x=0\), the velocity \(v\) is zero. What is the relation between velocity \(v\) and position \(x\) ?

141182 Particle \(\mathbf{A}\) (which was located at the origin at time \(t=0\) ) is moving along the \(x\) - axis with a constant speed of \(1 \mathrm{~m} / \mathrm{s}\). Location of particle \(B\) which is moving along the \(\mathrm{Y}\) - axis is given by \(y\) \(=c t^{2}\), where \(c=1 \mathrm{~m} / \mathrm{s}^{2}\). Find the speed of particle \(A\) relative to particle \(B\) at \(t=1\) sec.

141179 Two towns \(X\) and \(Y\) are connected by a regular bus service. \(A\) bus leaves in either direction at every \(t=T\) minutes. A man moving with some speed in the direction \(\mathrm{X}\) to \(\mathrm{Y}\) finds that a bus goes past him every \(t=t_{1}\) minutes in the direction of his motion, and every \(t=t_{2}\) minutes in the opposite direction. Then \(T\) is given by

141180 The co-ordinates \((x, y)\) of a moving particle at any time ' \(t\) ' are given by \(x=\alpha t^{3}\) and \(y=\beta t^{3}\). The speed of the particle at time ' \(t\) ' is given by

141181 Acceleration a is given in terms of position \(x\) as \(a=2 x \mathrm{~m} / \mathrm{s}^{2}\). At \(x=0\), the velocity \(v\) is zero. What is the relation between velocity \(v\) and position \(x\) ?

141182 Particle \(\mathbf{A}\) (which was located at the origin at time \(t=0\) ) is moving along the \(x\) - axis with a constant speed of \(1 \mathrm{~m} / \mathrm{s}\). Location of particle \(B\) which is moving along the \(\mathrm{Y}\) - axis is given by \(y\) \(=c t^{2}\), where \(c=1 \mathrm{~m} / \mathrm{s}^{2}\). Find the speed of particle \(A\) relative to particle \(B\) at \(t=1\) sec.

141179 Two towns \(X\) and \(Y\) are connected by a regular bus service. \(A\) bus leaves in either direction at every \(t=T\) minutes. A man moving with some speed in the direction \(\mathrm{X}\) to \(\mathrm{Y}\) finds that a bus goes past him every \(t=t_{1}\) minutes in the direction of his motion, and every \(t=t_{2}\) minutes in the opposite direction. Then \(T\) is given by

141180 The co-ordinates \((x, y)\) of a moving particle at any time ' \(t\) ' are given by \(x=\alpha t^{3}\) and \(y=\beta t^{3}\). The speed of the particle at time ' \(t\) ' is given by

141181 Acceleration a is given in terms of position \(x\) as \(a=2 x \mathrm{~m} / \mathrm{s}^{2}\). At \(x=0\), the velocity \(v\) is zero. What is the relation between velocity \(v\) and position \(x\) ?

141182 Particle \(\mathbf{A}\) (which was located at the origin at time \(t=0\) ) is moving along the \(x\) - axis with a constant speed of \(1 \mathrm{~m} / \mathrm{s}\). Location of particle \(B\) which is moving along the \(\mathrm{Y}\) - axis is given by \(y\) \(=c t^{2}\), where \(c=1 \mathrm{~m} / \mathrm{s}^{2}\). Find the speed of particle \(A\) relative to particle \(B\) at \(t=1\) sec.