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Q. No.Two cars \(P \) and \(Q\) move along the same straight road in the same direction. For \( t \ge 0, \) the acceleration of car \(P \) varies linearly with time, whereas car \(Q\) moves with a constant acceleration. At \(t=0 ,\) both cars are at the same position. The maximum possible number of times the two cars can be at the same position (including the instant \(t=0 \)) is:
1. \(3\)
2. \(2\)
3. \(1\)
4. Infinite
1. \(3\)
2. \(2\)
3. \(1\)
4. Infinite
Subtopic: Non Uniform Acceleration |
Level 4: Below 35%
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Two cars are moving towards each other, each with a speed of \(20\text{ m/s}.\) When they are \(300\text{ m}\) apart, both drivers apply the brakes simultaneously, causing each car to decelerate uniformly at \(2\text{ m/s}^2.\) What will be the distance between the two cars after both have come to rest?
1. \(200\text{ m}\)
2. \(50\text{ m}\)
3. \(100\text{ m}\)
4. \(25\text{ m}\)
1. \(200\text{ m}\)
2. \(50\text{ m}\)
3. \(100\text{ m}\)
4. \(25\text{ m}\)
Subtopic: Non Uniform Acceleration |
79%
Level 2: 60%+
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A ball is thrown upward with an initial velocity \(v_0\) from the surface of the earth. The motion of the ball is affected by a drag force equal to \(myv^2\) (where \(m\) is mass of the ball, \(v\) is its instantaneous velocity and \(y\) is a constant). The time taken by the ball to rise to its zenith (maximum height) is:
1. \( \dfrac{1}{\sqrt{y g}} \tan ^{-1}\left(\sqrt{\dfrac{y}{g}} v_0\right) \)
2. \( \dfrac{1}{\sqrt{2 y g}} \tan ^{-1}\left(\sqrt{\dfrac{2 y}{g} }v_0\right) \)
3. \( \dfrac{1}{\sqrt{y g}} \sin ^{-1}\left(\sqrt{\dfrac{y}{g}} v_0\right) \)
4. \( \dfrac{1}{\sqrt{y g}}\ln\left(1+\sqrt{\dfrac{y}{g}} v_0\right)\)
1. \( \dfrac{1}{\sqrt{y g}} \tan ^{-1}\left(\sqrt{\dfrac{y}{g}} v_0\right) \)
2. \( \dfrac{1}{\sqrt{2 y g}} \tan ^{-1}\left(\sqrt{\dfrac{2 y}{g} }v_0\right) \)
3. \( \dfrac{1}{\sqrt{y g}} \sin ^{-1}\left(\sqrt{\dfrac{y}{g}} v_0\right) \)
4. \( \dfrac{1}{\sqrt{y g}}\ln\left(1+\sqrt{\dfrac{y}{g}} v_0\right)\)
Subtopic: Non Uniform Acceleration |
Level 3: 35%-60%
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Q. No.
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