03. Equation of Motion
Motion in One Dimensions

141718 A body starts from rest, under the action of an engine working at a constant power and moves along a straight line. The displacement \(S\) is given as a function of time \((t)\) as

1 \(\mathrm{S}=\mathrm{at}+\mathrm{bt}^{2}\), \(\mathrm{a}\) and \(\mathrm{b}\) are constants
2 \(\mathrm{S}=\mathrm{bt}^{2}, \mathrm{~b}\) is a constant
3 \(\mathrm{S}=\mathrm{at}^{3 / 2}\), a is a constant
4 \(\mathrm{S}=\) at, \(\mathrm{a}\) is a constant
Motion in One Dimensions

141719 In a car race on a straight path, car \(A\) takes a time \(t\) less than car \(B\) at the finish and passes finishing point with a speed ' \(v\) ' more than that of car \(B\). Both the cars start from rest and travel with constant acceleration \(a_{1}\) and \(a_{2}\) respectively. Then ' \(v\) ' is equal to

1 \(\frac{2 a_{1} a_{2}}{a_{1}+a_{2}} t\)
2 \(\sqrt{2 a_{1} a_{2}} t\)
3 \(\sqrt{a_{1} a_{2}} t\)
4 \(\frac{a_{1}+a_{2}}{2} t\)
Motion in One Dimensions

141720 A boy can throw a ball obliquely to a maximum horizontal distance ' \(x\) ' while standing on the ground. If he throws the same ball from the top of a tower of height ' \(x\) ' at an angle of \(4^{\circ}\) above the horizontal from the foot of the tower, the ball hits the ground at a distance
(Assume same initial speeds )

1 \(\mathrm{x}(1+\sqrt{2})\)
2 \(\frac{x}{2}(1+\sqrt{3})\)
3 \(\mathrm{x}(1+\sqrt{4})\)
4 \(\frac{X}{2}(1+\sqrt{5})\)
Motion in One Dimensions

141721 In the given velocity \((V)\) versus time \((t)\) graph, accelerated and decelerated motions are respectively represented by line segments
original image

1 \(\mathrm{CD}\) and \(\mathrm{BC}\)
2 \(\mathrm{BC}\) and \(\mathrm{AB}\)
3 \(\mathrm{CD}\) and \(\mathrm{AB}\)
4 \(\mathrm{AB}\) and \(\mathrm{CD}\)
Motion in One Dimensions

141718 A body starts from rest, under the action of an engine working at a constant power and moves along a straight line. The displacement \(S\) is given as a function of time \((t)\) as

1 \(\mathrm{S}=\mathrm{at}+\mathrm{bt}^{2}\), \(\mathrm{a}\) and \(\mathrm{b}\) are constants
2 \(\mathrm{S}=\mathrm{bt}^{2}, \mathrm{~b}\) is a constant
3 \(\mathrm{S}=\mathrm{at}^{3 / 2}\), a is a constant
4 \(\mathrm{S}=\) at, \(\mathrm{a}\) is a constant
Motion in One Dimensions

141719 In a car race on a straight path, car \(A\) takes a time \(t\) less than car \(B\) at the finish and passes finishing point with a speed ' \(v\) ' more than that of car \(B\). Both the cars start from rest and travel with constant acceleration \(a_{1}\) and \(a_{2}\) respectively. Then ' \(v\) ' is equal to

1 \(\frac{2 a_{1} a_{2}}{a_{1}+a_{2}} t\)
2 \(\sqrt{2 a_{1} a_{2}} t\)
3 \(\sqrt{a_{1} a_{2}} t\)
4 \(\frac{a_{1}+a_{2}}{2} t\)
Motion in One Dimensions

141720 A boy can throw a ball obliquely to a maximum horizontal distance ' \(x\) ' while standing on the ground. If he throws the same ball from the top of a tower of height ' \(x\) ' at an angle of \(4^{\circ}\) above the horizontal from the foot of the tower, the ball hits the ground at a distance
(Assume same initial speeds )

1 \(\mathrm{x}(1+\sqrt{2})\)
2 \(\frac{x}{2}(1+\sqrt{3})\)
3 \(\mathrm{x}(1+\sqrt{4})\)
4 \(\frac{X}{2}(1+\sqrt{5})\)
Motion in One Dimensions

141721 In the given velocity \((V)\) versus time \((t)\) graph, accelerated and decelerated motions are respectively represented by line segments
original image

1 \(\mathrm{CD}\) and \(\mathrm{BC}\)
2 \(\mathrm{BC}\) and \(\mathrm{AB}\)
3 \(\mathrm{CD}\) and \(\mathrm{AB}\)
4 \(\mathrm{AB}\) and \(\mathrm{CD}\)
Motion in One Dimensions

141718 A body starts from rest, under the action of an engine working at a constant power and moves along a straight line. The displacement \(S\) is given as a function of time \((t)\) as

1 \(\mathrm{S}=\mathrm{at}+\mathrm{bt}^{2}\), \(\mathrm{a}\) and \(\mathrm{b}\) are constants
2 \(\mathrm{S}=\mathrm{bt}^{2}, \mathrm{~b}\) is a constant
3 \(\mathrm{S}=\mathrm{at}^{3 / 2}\), a is a constant
4 \(\mathrm{S}=\) at, \(\mathrm{a}\) is a constant
Motion in One Dimensions

141719 In a car race on a straight path, car \(A\) takes a time \(t\) less than car \(B\) at the finish and passes finishing point with a speed ' \(v\) ' more than that of car \(B\). Both the cars start from rest and travel with constant acceleration \(a_{1}\) and \(a_{2}\) respectively. Then ' \(v\) ' is equal to

1 \(\frac{2 a_{1} a_{2}}{a_{1}+a_{2}} t\)
2 \(\sqrt{2 a_{1} a_{2}} t\)
3 \(\sqrt{a_{1} a_{2}} t\)
4 \(\frac{a_{1}+a_{2}}{2} t\)
Motion in One Dimensions

141720 A boy can throw a ball obliquely to a maximum horizontal distance ' \(x\) ' while standing on the ground. If he throws the same ball from the top of a tower of height ' \(x\) ' at an angle of \(4^{\circ}\) above the horizontal from the foot of the tower, the ball hits the ground at a distance
(Assume same initial speeds )

1 \(\mathrm{x}(1+\sqrt{2})\)
2 \(\frac{x}{2}(1+\sqrt{3})\)
3 \(\mathrm{x}(1+\sqrt{4})\)
4 \(\frac{X}{2}(1+\sqrt{5})\)
Motion in One Dimensions

141721 In the given velocity \((V)\) versus time \((t)\) graph, accelerated and decelerated motions are respectively represented by line segments
original image

1 \(\mathrm{CD}\) and \(\mathrm{BC}\)
2 \(\mathrm{BC}\) and \(\mathrm{AB}\)
3 \(\mathrm{CD}\) and \(\mathrm{AB}\)
4 \(\mathrm{AB}\) and \(\mathrm{CD}\)
Motion in One Dimensions

141718 A body starts from rest, under the action of an engine working at a constant power and moves along a straight line. The displacement \(S\) is given as a function of time \((t)\) as

1 \(\mathrm{S}=\mathrm{at}+\mathrm{bt}^{2}\), \(\mathrm{a}\) and \(\mathrm{b}\) are constants
2 \(\mathrm{S}=\mathrm{bt}^{2}, \mathrm{~b}\) is a constant
3 \(\mathrm{S}=\mathrm{at}^{3 / 2}\), a is a constant
4 \(\mathrm{S}=\) at, \(\mathrm{a}\) is a constant
Motion in One Dimensions

141719 In a car race on a straight path, car \(A\) takes a time \(t\) less than car \(B\) at the finish and passes finishing point with a speed ' \(v\) ' more than that of car \(B\). Both the cars start from rest and travel with constant acceleration \(a_{1}\) and \(a_{2}\) respectively. Then ' \(v\) ' is equal to

1 \(\frac{2 a_{1} a_{2}}{a_{1}+a_{2}} t\)
2 \(\sqrt{2 a_{1} a_{2}} t\)
3 \(\sqrt{a_{1} a_{2}} t\)
4 \(\frac{a_{1}+a_{2}}{2} t\)
Motion in One Dimensions

141720 A boy can throw a ball obliquely to a maximum horizontal distance ' \(x\) ' while standing on the ground. If he throws the same ball from the top of a tower of height ' \(x\) ' at an angle of \(4^{\circ}\) above the horizontal from the foot of the tower, the ball hits the ground at a distance
(Assume same initial speeds )

1 \(\mathrm{x}(1+\sqrt{2})\)
2 \(\frac{x}{2}(1+\sqrt{3})\)
3 \(\mathrm{x}(1+\sqrt{4})\)
4 \(\frac{X}{2}(1+\sqrt{5})\)
Motion in One Dimensions

141721 In the given velocity \((V)\) versus time \((t)\) graph, accelerated and decelerated motions are respectively represented by line segments
original image

1 \(\mathrm{CD}\) and \(\mathrm{BC}\)
2 \(\mathrm{BC}\) and \(\mathrm{AB}\)
3 \(\mathrm{CD}\) and \(\mathrm{AB}\)
4 \(\mathrm{AB}\) and \(\mathrm{CD}\)