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Physics · MOTION IN A STRAIGHT LINE
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Physics · MOTION IN A STRAIGHT LINE
A ball is dropped from a height of \( 90\text{ m} \) on a horizontal floor. At each collision with the floor, the ball loses one tenth (\( 1/10 \)) of its speed. What is the maximum height reached by the ball after its second collision with the floor? (Take \( g = 9.8\text{ m s}^{-2} \))
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A man walks on a straight road from his home to a market \( 2.5\text{ km} \) away with a speed of \( 5\text{ km h}^{-1} \). Finding the market closed, he instantly turns around and walks back home with a speed of \( 7.5\text{ km h}^{-1} \). What are the magnitude of average velocity and average speed of the man over the time interval from \( 0 \) to \( 40\text{ min} \)?
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Consider the following statements regarding kinematics equations and graphs: (A) The equation \( v = v_0 + at \) is valid only for constant acceleration. (B) The position-time graph for zero acceleration is a straight line parallel to the time axis. (C) Free fall near Earth's surface is an example of motion with uniform acceleration. (D) The velocity-time curve can have sharp instantaneous breaks in real physical scenarios. How many of the above statements are correct?
Read answer →Physics · MOTION IN A STRAIGHT LINE
A particle moves along a straight line with position \( x(t) = t^3 - 6t^2 + 9t + 2 \) (where \( x \) is in meters and \( t \) is in seconds). Determine the ratio of the total distance traveled by the particle to the magnitude of its displacement during the time interval from \( t = 0 \text{ s} \) to \( t = 2 \text{ s} \).
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A police van moving on a highway at \( 30\text{ km/h} \) fires a bullet at a thief's car speeding away in the same direction at \( 192\text{ km/h} \). If the muzzle speed of the bullet is \( 150\text{ m/s} \), with what speed does the bullet hit the thief's car?
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A ball is thrown vertically upwards with a velocity of \( 20\text{ m s}^{-1} \) from the top of a building. Taking \( g = 10\text{ m s}^{-2} \), what is the maximum height reached above the point of launch?
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Consider the following statements regarding one-dimensional motion of a body: (A) A body with zero speed at an instant can have non-zero acceleration at that instant. (B) A body with zero speed at an instant can have non-zero velocity at that instant. (C) A body moving with constant speed in a straight line must have zero acceleration. (D) A body with positive acceleration must always be speeding up. Which of the above statements are correct?
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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): Equations of kinematics can be derived using calculus by integrating acceleration with respect to time. Reason (R): Differentiation and integration are inverse mathematical operations. In the light of the above statements, choose the correct answer from the options given below:
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A particle moves along the x-axis such that its position is given by \( x = a + b t^2 \), where \( a = 8.5 \text{ m} \) and \( b = 2.5 \text{ m/s}^2 \). A second particle moves along the same line starting from rest at origin with constant acceleration \( c \). If the average velocity of the first particle between \( t = 2.0 \text{ s} \) and \( t = 4.0 \text{ s} \) equals the instantaneous velocity of the second particle at \( t = 3.0 \text{ s} \), find the value of \( c \).
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Match List-I with List-II: List-I List-II A Average velocity I \( \lim_{\Delta t \to 0} \frac{\Delta v}{\Delta t} \) B Instantaneous acceleration II \( \frac{\Delta x}{\Delta t} \) C Stopping distance III \( \sqrt{\frac{2d}{g}} \) D Reaction time IV \( \frac{v_0^2}{2a} \) Choose the correct answer from the options given below:
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The kinematic relation \( v^2 = v_0^2 + 2ax \) is valid under which of the following conditions?
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Match List-I with List-II for calculus relations in kinematics: List-I List-II A \( \frac{dx}{dt} \) I Displacement in time interval \( [t_1, t_2] \) B \( \frac{dv}{dt} \) II Instantaneous velocity C \( v \frac{dv}{dx} \) III Acceleration in terms of position D \( \int_{t_1}^{t_2} v \, dt \) IV Instantaneous acceleration Choose the correct answer from the options given below:
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The velocity of a particle moving along the x-axis is given by \( v = (3.0 t^2 - 6.0 t + 2.0)\text{ m s}^{-1} \). At what instant of time \( t > 0 \) is the instantaneous acceleration of the particle zero?
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An object moves with a constant velocity \( u \) for a time interval \( T \). Immediately after, it accelerates uniformly at a rate \( a \) for an equal time interval \( T \). What is the total displacement covered by the object in the total time \( 2T \)?
Read answer →Physics · MOTION IN A STRAIGHT LINE
Consider the following statements regarding motion in a straight line: (A) The slope of the position-time graph gives velocity. (B) The area under the velocity-time graph gives displacement. (C) The slope of the velocity-time graph gives acceleration. (D) The area under the acceleration-time graph gives distance. Which of the above statements are correct?
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Match List-I with List-II: List-I (1D Motion Graph Anomaly) List-II (Physical Impossibility Reason) A Total path length decreasing with time I Speed is intrinsically non-negative B Speed vs time graph with negative values II Total distance traversed can never decrease C Position-time graph forming a closed loop III Particle would have two velocities at the same instant D Velocity-time graph forming a closed loop IV Particle would occupy two positions at the same instant Choose the correct answer from the options given below:
Read answer →Physics · MOTION IN A STRAIGHT LINE
A train accelerates uniformly from rest at rate \( a_1 = 1.0 \text{ m/s}^2 \) for a time \( t_1 \), then travels at a constant maximum velocity \( v_{\max} \) for a time interval \( t_2 = 10 \text{ s} \), and finally decelerates uniformly at rate \( a_2 = 2.0 \text{ m/s}^2 \) until coming to rest. If the total distance covered is \( 500 \text{ m} \), find \( v_{\max} \).
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If air resistance is neglected, an object dropped near the surface of the Earth is said to be in free fall. The acceleration of a freely falling body is equal to:
Read answer →Physics · MOTION IN A STRAIGHT LINE
A man walks on a straight road from his home to a market \( 2.5\text{ km} \) away at a speed of \( 5\text{ km/h} \). Finding the market closed, he instantly turns and walks back home at a speed of \( 7.5\text{ km/h} \). Match the time intervals in List-I with the corresponding values of average speed/velocity in List-II: List-I List-II A Average speed in interval \( 0\text{ to }30\text{ min} \) I \( 0\text{ km/h} \) B Average speed in interval \( 0\text{ to }50\text{ min} \) II \( 5.625\text{ km/h} \) C Magnitude of average velocity in interval \( 0\text{ to }50\text{ min} \) III \( 5\text{ km/h} \) D Average speed in interval \( 0\text{ to }40\text{ min} \) IV \( 6\text{ km/h} \) Choose the correct answer from the options given below:
Read answer →Physics · MOTION IN A STRAIGHT LINE
Given below are two statements: Statement I: The slope of a position-time graph at any point gives the instantaneous velocity at that instant. Statement II: The slope of a velocity-time graph at any point gives the instantaneous acceleration at that instant. In the light of the above statements, choose the most appropriate answer from the options given below:
Read answer →Physics · MOTION IN A STRAIGHT LINE
In a reaction time experiment using a ruler drop, a person catches a vertically dropped ruler after a displacement of \( d_1 = 20\text{ cm} \). In a second trial under fatigue, the person's reaction time increases by \( 25\% \). What is the distance \( d_2 \) measured on the ruler in the second trial?
Read answer →Physics · MOTION IN A STRAIGHT LINE
Which of the kinematic equations correctly relates final velocity \( v \), initial velocity \( v_0 \), acceleration \( a \), and time \( t \)?
Read answer →Physics · MOTION IN A STRAIGHT LINE
