Answer : (c), (d), and (e) are the correct formulae for characterizing the particle's motion (f) The given graph has a non-uniform slope. As a result, the formulas in (a), (b), and (e) are unable to...
The speed-time graph of a particle moving along a fixed direction is shown in the figure. Obtain the distance traversed by the particle between (a) t = 0 s to 10 s, (b) t = 2 s to 6 s.
Answer : (a) According to the diagram above the distance moved by the particle between t = 0s and t = 10s is equal to the are of the triangle shown above. So, we can write Distance transversed by...
Two stones are thrown up simultaneously from the edge of a cliff 200 m high with initial speeds of 15 m s–1 and 30 m s–1. Verify that the graph shown in Fig. 3.27 correctly represents the time variation of the relative position of the second stone with respect to the first. Neglect air resistance and assume that the stones do not rebound after hitting the ground. Take g = 10 m s–2. Give the equations for the linear and curved parts of the plot.
Ans. For the first stone, it is given that the acceleration is a = –g = – 10 m/s2 And the initial velocity is uI = 15 m/s Using the expression of equation of motion => s1 = s0 + u1t + (1/2)at2...
On a long horizontally moving belt figure, a child runs to and fro with a speed 9 km h–1 (with respect to the belt) between his father and mother located 50 m apart on the moving belt. The belt moves with a speed of 4 km h–1. For an observer on a stationary platform outside, what is the (a) speed of the child running in the direction of motion of the belt ?. (b) speed of the child running opposite to the direction of motion of the belt? (c) time taken by the child in (a) and (b)? Which of the answers alter if motion is viewed by one of the parents?
Answer - According to the question, speed of child is 9 km h-1 speed of the belt is 4 km h-1 (a) When the boy runs in the belt's direction of motion, his speed as measured by a stationary observer...
A boy standing on a stationary lift (open from above) throws a ball upwards with the maximum initial speed he can, equal to 49 m s-1. How much time does the ball take to return to his hands? If the lift starts moving up with a uniform speed of 5 m s-1 and the boy again throws the ball up with the maximum speed he can, how long does the ball take to return to his hands?
Ans: According to the question, the initial velocity of the ball (u) is 49 m/s Case 1 : When the lift is stationary, the boy throws the ball upwards. The positive direction is considered to be...
A three-wheeler starts from rest, accelerates uniformly with 1 m s–2 on a straight road for 10 s, and then moves with uniform velocity. Plot the distance covered by the vehicle during the nth second (n = 1,2,3….) versus n. What do you expect this plot to be during accelerated motion: a straight line or a parabola?
Ans. Expression for the distance travelled by a body in the nth second, for a straight line is given as follows - SN = u + a (2n – 1)/2 ...
The following figure gives a speed-time graph of a particle in motion along a constant direction. Three equal intervals of time are shown. In which interval is the average acceleration greatest in magnitude? In which interval is the average speed greatest? Choosing the positive direction as the constant direction of motion, give the signs of v and a in the three intervals. What are the accelerations at points A, B, C and D?
The slope of the particle's speed-time graph provides information on the particle's acceleration. The slope of the graph in the specified interval determines the magnitude of the particle's average...
The figure gives the x-t plot of a particle in one-dimensional motion. Three different equal intervals of time are shown. In which interval is the average speed greatest, and in which is it the least? Give the sign of average velocity for each interval.
Answer - Interval 2 (Largest), Interval 3 (Greatest) (Least) Positive (Intervals 1 & 2), Negative (Intervals 3 & 4) (Interval 3) The slope of the graph at a given time interval is used to...
The following figure gives the x-t plot of a particle executing one-dimensional simple harmonic motion. (You will learn about this motion in more detail in Chapter 14). Give the signs of position, velocity and acceleration variables of the particle at t = 0.3 s, 1.2 s, – 1.2 s.
Ans. In Simple harmonic Motion, acceleration (a) is given as => a = – ω2 x —-(1) where ω is the angular frequency (i) We are given that, at t = 0.3 s,...
Suggest a suitable physical situation for each of the following graphs
Answer - (a)The graph looks like a ball being kicked, then hitting a wall and bouncing back at a slower speed. The ball then travels in the opposite direction and collides with the opposing wall,...
A police van moving on a highway with a speed of 30 km h–1 fires a bullet at a thief’s car speeding away in the same direction with a speed of 192 km h–1. If the muzzle speed of the bullet is 150 m s–1, with what speed does the bullet hit the thief’s car? (Note: Obtain that speed which is relevant for damaging the thief’s car).
Answer - according to the question, the speed of the police van is 30 km/h Or, 30 x (5/18) = 25/3 m/s And the speed of a thief’s car is 192 km/h or, 192 x (5/18) = 160/3 m/s It is also given that...
The figure shows the x-t plot of the one-dimensional motion of a particle. Is it correct to say from the graph shows that the particle moves in a straight line for t < 0 and on a parabolic path for t >0? If not, suggest a suitable physical context for this graph.
Answer - The position-time graph is used to determine the position of a body at any given time, but not to establish its trajectory. Context - At time t = 0, a body is dropped from a tower (x = 0)....
Look at the graphs (a) to (d) carefully and state, with reasons, which of these cannot possibly represent the one-dimensional motion of a particle.
Answer - There is no one-dimensional mobility in any of the four graphs. (a) Displays two positions at once, which is impossible. (b) At the same moment, a particle cannot have velocity in two...
In Exercises 3.13 and 3.14, we have carefully distinguished between average speed and magnitude of average velocity. No such distinction is necessary when we consider the instantaneous speed and the magnitude of velocity. The instantaneous speed is always equal to the magnitude of instantaneous velocity. Why?
Answer - Because the magnitude of the displacement is functionally equal to the distance traversed by the particle, instantaneous velocity and instantaneous speed are equal for a short period of...
A man walks on a straight road from his home to a market 2.5 km away with a speed of 5 km/h. Finding the market closed, he instantly turns and walks back home with a speed of 7.5 km h–1. What is the (a) Magnitude of average velocity, and (b) Average speed of the man over the interval of time (i) 0 to 30 min, (ii) 0 to 50 min, (iii) 0 to 40 min? [Note: You will appreciate from this exercise why it is better to define average speed as total path length divided by time, and not as the magnitude of average velocity. You would not like to tell the tired man on his return home that his average speed was zero !]
Answer - According to the question, distance to the market is 2.5 km or 2500 m and the speed of man walking to market is 5 km/h Or, 5 x (5/18) = 1.388 m/s It is also provided that the speed of man...
Provide clear explanations and examples to distinguish between: ( a ) The total length of a path covered by a particle and the magnitude of displacement over the same interval of time. ( b ) The magnitude of average velocity over an interval of time, and the average speed over the same interval. [Average speed of a particle over an interval of time is defined as the total path length divided by the time interval]. In ( a ) and ( b ) compare and find which among the two quantity is greater. When can the given quantities be equal? [For simplicity, consider one-dimensional motion only].
Answer - (a) Consider a football, which is passed to player B by player A and then immediately kicked back to player A along the same path. The magnitude of the ball's displacement is now 0 because...
A ball is dropped from a height of 90 m on a floor. At each collision with the floor, the ball loses one-tenth of its speed. Plot the speed-time graph of its motion between t = 0 to 12 s.
Answer - According to the question, the drop height of the ball is 90 m and the initial velocity of the ball (u) is zero. Let v denote the final velocity of the ball Then, making use of the equation...
Read each statement below carefully and state with reasons and examples, if it is true or false; A particle in one-dimensional motion (a) with zero speed at an instant may have non-zero acceleration at that instant (b) with zero speed may have non-zero velocity, (c) with constant speed must have zero acceleration, (d) with positive value of acceleration must be speeding up
Answer - (a) True It is true that when an object is hurled vertically into the air, its speed is zero at maximum height. It does, however, have an acceleration equal to the downward acceleration...
A player throws a ball upwards with an initial speed of 29.4 m/s. (c) Choose the x = 0 m and t = 0 s to be the location and time of the ball at its highest point, vertically downward direction to be the positive direction of the x-axis, and give the signs of position, velocity and acceleration of the ball during its upward, and downward motion. (d) To what height does the ball rise and after how long does the ball return to the player’s hands? (Take g = 9.8 m s–2 and neglect air resistance).
Answer - (c) If we assume the highest point of ball motion to be x = 0, t = 0, and the vertically downward direction of the x-axis to be +ve, then (i) Before reaching the highest point position,x =...
A player throws a ball upwards with an initial speed of 29.4 m/s. (a) What is the direction of acceleration during the upward motion of the ball? (b) What are the velocity and acceleration of the ball at the highest point of its motion?
Answer - (a) Gravitational acceleration constantly acts downwards towards the Earth's center. (b) The ball's velocity will be zero at its highest point of motion, but the acceleration due to gravity...
Two towns A and B are connected by regular bus service with a bus leaving in either direction every T minutes. A man cycling with a speed of 20 km h–1 in the direction A to B notices that a bus goes past him every 18 min in the direction of his motion, and every 6 min in the opposite direction. What is the period T of the bus service and with what speed (assumed constant) do the buses ply on the road?
Answer - Let the speed of each bus be denoted by Vb speed of the cyclist be Vc. And according to the question, Vc = 20 km/h Buses travelling in the same direction as cyclists have a relative...
On a two-lane road, car A is travelling at a speed of 36 km/h. Two cars B and C approach car A in opposite directions with a speed of 54 km/h each. At a certain instant, when the distance AB is equal to AC, both being 1 km, B decides to overtake A before C does. What minimum acceleration of car B is required to avoid an accident?
Ans: According to the question speed of car A is 36 km/h or, 36 x (5/8) = 10 m/s And the speed of car B is 54 km/h Or, 54 x (5/18) = 15 m/s And the speed of car C is – 54 km/h Or, -54 x (5/18) = -15...
Two trains A and B of length 400 m each are moving on two parallel tracks with a uniform speed of 72 km h–1 in the same direction, with A ahead of B. The driver of B decides to overtake A and accelerates by 1 m s–2. If after 50 s, the guard of B just brushes past the driver of A, what was the original distance between them?
Ans: According to the question, length of the train A and B is 400 m and the speed of both the trains is given = 72 km/h = 72 x (5/18) = 20m/s Using the following expression, s = ut + (1/2)at2 We...
A car moving along a straight highway with a speed of 126 km h–1 is brought to a stop within a distance of 200 m. What is the retardation of the car (assumed uniform), and how long does it take for the car to stop?
Ans. According to the question, the initial velocity of the car is u = 126 km/h ( we will change it in meter/sec as follows) u = 126 × (5/18) m/s Therefore, u = 35 m/s And the final velocity of the...
A jet airplane travelling at the speed of 500 km/h ejects its products of combustion at the speed of 1500 km/h relative to the jet plane. What is the speed of the latter with respect to an observer on the ground?
Answer : According to the question, the speed of the jet airplane (VA) is 500 km/h And the speed of ejection of combustion products relative to the jet plane is given by VB – VA= – 1500 km/h Here,...
A drunkard walking in a narrow lane takes 5 steps forward and 3 steps backwards, followed again by 5 steps forward and 3 steps backwards, and so on. Each step is 1m long and requires 1 s. Plot the x-t graph of his motion. Determine graphically and otherwise how long the drunkard takes to fall in a pit 13 m away from the start.
Solution : One second is the time it takes to take one step. He walks ahead for 5 seconds, covering a distance of 5 meters, and then returns 3 meters in the next 3 seconds. As a result, he covers 2m...
A woman starts from her home at 9.00 am, walks at a speed of 5 km/h on a straight road up to her office 2.5 km away, stays at the office up to 5.00 pm, and returns home by auto with a speed of 25 km/h. Choose suitable scales and plot the x-t graph of her motion.
Answer - According to the question, distance up to the woman's office is 2.5 km And woman's walking speed is 5 km/hTherefore by using the distance-time relation, we can find the time taken by woman...
The position-time (x-t) graphs for two children A and B returning from their school O to their homes P and Q respectively are shown in Fig. Choose the correct entries in the brackets below ;
(a) (A/B) lives closer to the school than (B/A) (b) (A/B) starts from the school earlier than (B/A) (c) (A/B) walks faster than (B/A) (d) A and B reach home at the (same/different) time (e) (A/B)...
In which of the following examples of motion, can the body be considered
approximately a point object:
(a) a railway carriage moving without jerks between two stations.(b) a monkey sitting on top of a man cycling smoothly on a circular track.(c) a spinning cricket ball that turns sharply on hitting...