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MOTION IN A STRAIGHT LINE
Study Material
MOTION IN A STRAIGHT LINE
Very Short Answer Questions
Q1. Define instantaneous velocity. How is it determined graphically?
Q2. Differentiate distance from displacement.
Q3. What is the difference between average speed and instantaneous speed?
Q4. A car moves with uniform acceleration. Write the relation among displacement, initial velocity, acceleration, and time.
Q5. What do you mean by rectilinear motion? Give one example.
Q6. Define average acceleration. What are its SI units?
Q7. What do you mean by free fall? Mention the value and direction of acceleration in this case.
Q8. Why is instantaneous speed equal to the magnitude of instantaneous velocity?
Q9. Explain how the area under the velocity-time graph gives displacement.
Q10. Can a body have zero velocity and non-zero acceleration at the same time? Explain.
Q11. A car accelerates uniformly from \(10\,\mathrm{m\,s^{-1}}\) to \(20\,\mathrm{m\,s^{-1}}\) in \(5\,\mathrm{s}\). Calculate the acceleration.
Q12. An object is thrown vertically upwards with a velocity of \(30\,\mathrm{m\,s^{-1}}\). What will be its velocity after \(2\,\mathrm{s}\)? (Take \(g=9.8\,\mathrm{m\,s^{-2}}\))
Q13. A car moving at \(72\,\mathrm{km\,h^{-1}}\) is brought to rest in \(10\,\mathrm{s}\). Calculate the distance it covers before stopping.
Q14. The velocity of a particle is given by \(v(t)=3t^2\). Find its acceleration at \(t=2\,\mathrm{s}\).
Q15. A train starts from rest and attains a velocity of \(36\,\mathrm{km\,h^{-1}}\) in \(10\,\mathrm{s}\). Assuming uniform acceleration, calculate the acceleration and distance covered in this time.
Q16. A ball is dropped from a height of \(20\,\mathrm{m}\). Find the time it takes to reach the ground. (Take \(g=10\,\mathrm{m\,s^{-2}}\))
Q17. A man walks \(2\,\mathrm{km}\) in \(30\) minutes and returns in \(20\) minutes. What is his average speed for the entire journey?
Q18. An object moves with uniform acceleration and covers \(100\,\mathrm{m}\) in \(5\,\mathrm{s}\). If its initial velocity is \(4\,\mathrm{m\,s^{-1}}\), find the acceleration.
Q19. A bullet is fired horizontally from a police car moving at \(30\,\mathrm{km\,h^{-1}}\). If the muzzle speed of the bullet is \(150\,\mathrm{km\,h^{-1}}\), find the speed of the bullet relative to a thief's car moving ahead at \(192\,\mathrm{km\,h^{-1}}\).
Q20. A ruler falls freely and travels \(20\,\mathrm{cm}\) before being caught. Estimate the reaction time of the person. (Use \(g=10\,\mathrm{m\,s^{-2}}\))
Q1. Derive the equation: \(v=u+at\) using calculus.
Q2. Derive an expression for displacement under uniformly accelerated motion using velocity-time graph.
Q3. Derive the kinematic equation of motion: \(v^2=v_0^2+2ax\).
Q4. A ball is thrown vertically upwards with velocity \(20\,\mathrm{m\,s^{-1}}\) from a height of \(25\,\mathrm{m}\). Calculate the time taken to reach the ground.
Q5. Explain Galileo’s law of odd numbers with a suitable example.
Q6. A man walks \(2.5\,\mathrm{km}\) to market at a speed of \(5\,\mathrm{km\,h^{-1}}\) and returns at \(7.5\,\mathrm{km\,h^{-1}}\). Find his average speed and average velocity.
Q7. Plot a position-time graph for a body under uniform acceleration. Explain how to find velocity from it.
Q8. Explain with an example why instantaneous acceleration may be non-zero even when instantaneous velocity is zero.
Q9. Define reaction time. Describe an experiment to measure it using a ruler.
Q1. A man walks on a straight road from his home to a market \(2.5\,\mathrm{km}\) away with a speed of \(5\,\mathrm{km\,h^{-1}}\). Finding the market closed, he instantly turns and walks back home with a speed of \(7.5\,\mathrm{km\,h^{-1}}\). What is the (a) magnitude of average velocity and (b) average speed of the man over the time interval \(0\) to \(50\) min?
Q2. A car travels the first third of a distance with a speed of \(10\,\mathrm{km\,h^{-1}}\), the second third at \(20\,\mathrm{km\,h^{-1}}\) and the last third at \(60\,\mathrm{km\,h^{-1}}\). What is its mean speed over the entire distance?
Q3. A bullet moving with a speed of \(150\,\mathrm{m\,s^{-1}}\) strikes a tree and penetrates \(3.5\,\mathrm{cm}\) before stopping. What is the magnitude of its retardation in the tree and the time taken for it to stop after striking the tree?
Q4. A motorist drives north for \(30\) min at \(85\,\mathrm{km\,h^{-1}}\) and then stops for \(15\) min. He continues travelling north and covers \(130\,\mathrm{km}\) in \(2\) hours. What is his total displacement and average velocity?
Q5. A ball \(A\) is dropped from the top of a building and at the same time an identical ball \(B\) is thrown vertically upwards from the ground. When do the balls collide if the speed of \(A\) is twice that of \(B\)?
Q6. Drops of water fall at regular intervals from the roof of a building of height \(16\,\mathrm{m}\). The first drop strikes the ground at the same moment as the fifth drop leaves the roof. Find the distances between successive drops.
Q7. A hunter aims a gun at a monkey hanging from a tree some distance away. The monkey drops from the branch at the moment he fires the gun hoping to avoid the bullet. Explain why the monkey made a wrong move.
Q8. A food packet is dropped from an aeroplane, moving with a speed of \(360\,\mathrm{kmph}\) in a horizontal direction, from a height of \(500\,\mathrm{m}\). Find (i) its time of descent (ii) the horizontal distance between the point at which the food packet reaches the ground and the point above which it was dropped.
Q1. A car is moving along a straight line as shown in Fig. 2.2. It moves from \(O\) to \(P\) in \(18\,\mathrm{s}\) and returns from \(P\) to \(Q\) in \(6.0\,\mathrm{s}\). What is the average velocity and average speed of the car in going (a) from \(O\) to \(P\)? and (b) from \(O\) to \(P\) and back to \(Q\)?
Q2. The position of an object moving along x-axis is given by \(x=a+bt^2\) where \(a=8.5\,\mathrm{m}\), \(b=2.5\,\mathrm{m\,s^{-2}}\) and \(t\) is measured in seconds. What is its velocity at \(t=0\,\mathrm{s}\) and \(t=2.0\,\mathrm{s}\). What is the average velocity between \(t=2.0\,\mathrm{s}\) and \(t=4.0\,\mathrm{s}\)?
Q3. Obtain equations of motion for constant acceleration using method of calculus.
Q4. A ball is thrown vertically upwards with a velocity of \(20\,\mathrm{m\,s^{-1}}\) from the top of a multistorey building. The height of the point from where the ball is thrown is \(25.0\,\mathrm{m}\) from the ground. (a) How high will the ball rise? and (b) how long will it be before the ball hits the ground? Take \(g=10\,\mathrm{m\,s^{-2}}\).
Q5. Free-fall: Discuss the motion of an object under free fall. Neglect air resistance.
Q6. Galileo’s law of odd numbers: “The distances traversed, during equal intervals of time, by a body falling from rest, stand to one another in the same ratio as the odd numbers beginning with unity [namely 1: 3: 5: 7.....].” Prove it.
Q7. Stopping distance of vehicles: When brakes are applied to a moving vehicle, the distance it travels before stopping is called stopping distance. It is an important factor for road safety and depends on the initial velocity \(v_0\) and the braking capacity, or deceleration, \(-a\) that is caused by the braking. Derive an expression for the stopping distance of a vehicle in terms of \(v_0\) and \(a\).
Q8. Reaction time: When a situation demands our immediate action, it takes some time before we respond. Reaction time is the time a person takes to observe, think and act. For example, if a person is driving and suddenly a boy appears on the road, then the time elapsed before he applies the brakes of the car is the reaction time. Reaction time depends on the complexity of the situation and on an individual. You can measure your reaction time by a simple experiment. Take a ruler and ask your friend to drop it vertically through the gap between your thumb and forefinger. After you catch it, find the distance \(d\) travelled by the ruler. In a particular case, \(d\) was found to be \(21.0\,\mathrm{cm}\). Estimate reaction time.
Q9. Two parallel rail tracks run north-south. Train \(A\) moves north with a speed of \(54\,\mathrm{km\,h^{-1}}\) and train \(B\) moves south with a speed of \(90\,\mathrm{km\,h^{-1}}\). What is the (a) velocity of \(B\) with respect to \(A\), (b) velocity of ground with respect to \(B\), and (c) velocity of a monkey running on the roof of the train \(A\) against its motion (with a velocity of \(18\,\mathrm{km\,h^{-1}}\) with respect to the train \(A\)) as observed by a man standing on the ground?