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Physics · MOTION IN A STRAIGHT LINE
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Physics · MOTION IN A STRAIGHT LINE
Match List-I with List-II for motion under gravity (ball thrown vertically upward with initial speed \( v_0 \)): List-I List-II A Time taken to reach peak height I \( v_0 \) B Maximum height reached above launch point II \( \frac{2 v_0}{g} \) C Total time of flight to return to launch level III \( \frac{v_0}{g} \) D Speed upon returning to launch level IV \( \frac{v_0^2}{2g} \) Choose the correct answer from the options given below:
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Match List-I with List-II regarding graph features in one-dimensional motion: List-I List-II A Position-time curve concave upwards (\( d^2x/dt^2 > 0 \)) I Net displacement over time interval B Position-time curve concave downwards (\( d^2x/dt^2 < 0 \)) II Motion with negative acceleration turning back after stopping C v-t graph with negative slope crossing time axis III Motion with positive acceleration (\( a > 0 \)) D Area under v-t graph between \( t_1 \) and \( t_2 \) IV Motion with negative acceleration (\( a < 0 \)) Choose the correct answer from the options given below:
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A particle moves along a straight line with uniform acceleration \( a \). Its velocities at two points A and B are \( v_A = 10 \text{ m/s} \) and \( v_B = 30 \text{ m/s} \) respectively. Calculate the velocity of the particle as it passes through the midpoint C of the segment AB.
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A police van moving on a highway with a speed of \( 30\text{ km h}^{-1} \) fires a bullet at a thief's car speeding away in the same direction with a speed of \( 192\text{ km h}^{-1} \). If the muzzle speed of the bullet is \( 150\text{ m s}^{-1} \), with what speed does the bullet hit the thief's car?
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A particle starts from rest at \( t = 0 \) and moves in a straight line with an acceleration given by \( a = (3t + 2)\text{ m/s}^2 \), where \( t \) is in seconds. The velocity of the particle at \( t = 4\text{ s} \) is:
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Car A moves along a straight road with constant velocity \( v_A = 20 \text{ m/s} \). Car B is initially a distance \( d = 150 \text{ m} \) ahead of Car A. At \( t = 0 \), Car B starts from rest and accelerates in the same direction with constant acceleration \( a_B = 2.0 \text{ m/s}^2 \). Find the minimum distance of approach between the two cars.
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A body is released from rest from a great height and falls freely under gravity. The ratio of the distance covered by the body in the \( 1^{\text{st}} \), \( 2^{\text{nd}} \), \( 3^{\text{rd}} \), and \( 4^{\text{th}} \) second of its fall is:
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A body starting from rest moves with constant acceleration \( a \). If the time taken by the body to cover successive equal distance segments \( S \) are \( t_1, t_2, t_3 \dots \), then the ratio \( t_1 : t_2 : t_3 \) is:
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A bullet entering a wooden block with an initial velocity of \( 100\text{ m s}^{-1} \) comes to rest after penetrating a distance of \( 0.1\text{ m} \). Assuming uniform retardation, what is the magnitude of the deceleration of the bullet?
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A body starting from rest moves along a straight line with uniform acceleration. It covers a distance \( x_1 \) in the first \( t \) seconds and an additional distance \( x_2 \) in the next \( t \) seconds. The relation between \( x_1 \) and \( x_2 \) is:
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Referring to the schematic motion diagram shown in Fig. 2.6, a ball is thrown vertically upwards from point A (top of a building of height \( y_0 = 25 \text{ m} \)) with an initial speed \( v_0 = 20 \text{ m/s} \). It reaches its peak position B and then falls down to point C on the ground. Taking \( g = 10 \text{ m/s}^2 \), calculate the ratio of the time taken by the ball to travel from A to B (\( t_{AB} \)) to the time taken to travel from B to C (\( t_{BC} \)).
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Given below are two statements: Statement I: The average velocity of an object can be zero even if its average speed is non-zero. Statement II: The magnitude of average velocity is always equal to average speed. In the light of the above statements, choose the most appropriate answer from the options given below:
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A car completes the first one-third of a total distance \( d \) at speed \( 10\text{ m s}^{-1} \), the second one-third at \( 20\text{ m s}^{-1} \), and the final one-third at \( 30\text{ m s}^{-1} \). What is the average speed of the car over the entire distance?
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A ball is dropped from a height of \( 90\text{ m} \) on a floor. Taking \( g = 9.8\text{ m/s}^2 \), if the ball loses one-tenth of its speed at each collision with the floor, what is the speed of the ball just before the first collision and the height to which it rebounds after the first bounce?
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Consider the following characteristics of motion along a straight line: (A) Average velocity is the displacement divided by the total time interval. (B) Instantaneous velocity is the derivative of position with respect to time. (C) The area under the velocity-time graph represents acceleration. (D) In uniform motion, instantaneous speed equals average speed. Which of the above statements are correct?
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The velocity of an object is given by \( v = \frac{dx}{dt} \). When the position-time graph is a straight line inclined to the time axis, the instantaneous velocity is:
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A ball is thrown vertically upwards with a velocity of \( 20.0\text{ m s}^{-1} \) from the top of a building of height \( 25.0\text{ m} \) above the ground. Taking \( g = 10.0\text{ m s}^{-2} \), what is the maximum height reached by the ball above the ground level?
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Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): A body can have zero velocity and still be accelerating. Reason (R): Acceleration is the rate of change of velocity; at the highest point of a vertically thrown ball, velocity is zero while acceleration is \( g \) downwards. In the light of the above statements, choose the correct answer from the options given below:
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To measure reaction time, a student's friend drops a ruler vertically from rest between the student's fingers. The student catches the ruler after it travels a distance of \( 19.6\text{ cm} \). Taking \( g = 9.8\text{ m/s}^2 \), the reaction time of the student is:
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A ball is thrown vertically upwards from the top of a building of height \( 25 \text{ m} \) with an initial speed of \( 20 \text{ m/s} \). At the exact same instant, a second ball is dropped from rest from a point \( 45 \text{ m} \) directly above the ground. Taking \( g = 10 \text{ m/s}^2 \), find the time elapsed before the two balls cross each other in air.
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The SI unit of acceleration is:
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A ball projected vertically upwards from the edge of a cliff top takes \( t_1 = 2.0 \text{ s} \) to reach its peak height above the cliff. The total time taken by the ball from projection until it strikes the ground at the base of the cliff is \( T = 5.0 \text{ s} \). Taking \( g = 10 \text{ m/s}^2 \), calculate the height of the cliff.
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