Q. A man walks on a straight road from his home to a market 2.5 km away with a speed of $5km{h}^{-1}$. Finding the market closed, he instantly turns and walks back home with a speed of $7.5km{h}^{-1}$. What is the magnitude of average velocity?

1. 20 m/s
2. 10 m/s
3. 35 m/s
4. 0 m/s

Q. 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. above. 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) overtakes (B/A) on the road (once/twice).

Q. 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.

Q. Why did Vijay Singh say “Appearances can be deceptive”?

Q. 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 the ground.
(d) A tumbling beaker that has slipped off the edge of a table.

Q. Figure gives the x-t plot of a particle executing one-dimensional simple harmonic motion. Give the signs of position, velocity and acceleration variables of the particle at $t=0.3s,1.2s,-1.2s.$

Q. Suggest a suitable physical situation for each of the following graphs (Fig):

Q. A car moving along a straight highway with speed of $126km{h}^{-1}$ 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 ?

Q. A drunkard walking in a narrow lane takes 5 steps forward and 3 steps backward, followed again by 5 steps forward and 3 steps backward, and so on. Each step is 1 m 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.

Q. On a two-lane road, car $A$ is travelling with a speed of $36km{h}^{-1}$. Two cars $B$ and $C$ approach car $A$ in opposite directions with a speed of $54km{h}^{-1}$ each. At a certain instant, when the distance $AB$ is equal to $AC$, both being $1km,B$ decides to overtake $A$ before $C$ does. What minimum acceleration of car $B$ is required to avoid an accident?

Q. Explain clearly, with examples, the distinction between:
(a) Magnitude of displacement (sometimes called distance) over an interval of time, and the total length of path covered by a particle over the same interval.
(b) 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].

Q. A police van moving on a highway with a speed of $30km/hr$ fires a bullet at a thief's car speeding away in the same direction with a speed of $192km/hr$. If the muzzle speed of the bullet is $150m/s$, with what speed does the bullet hit the thief's car ? (Note:Obtain that speed which is relevant for damaging the thief's car).

Q. Look at the graphs (a) to (d) carefully and state, with reasons, which of these cannot possibly represent one-dimensional motion of a particle.

Q. A jet airplane travelling at the speed of $500km{h}^{-1}$ ejects its products of combustion at the speed of $1500km{h}^{-1}$ relative to the jet plane. What is the speed of the latter with respect to an observer on the ground ?

Q.

Q. A woman starts from her home at 9.00 am, walks with a speed of $5km{h}^{-1}$ 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 an auto with a speed of $25km{h}^{-1}$. Plot the position-time graph of the woman taking her home as origin.

Q. A player throws a ball upwards with an initial speed of $29.4m{s}^{-1}$.
(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 ?
(c) Choose 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 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 players hands ? (Take $g=9.8m/s^2$ and neglect air resistance).

Q. 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.

Q. 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.

Q. Figure shows the x-t plot of one-dimensional motion of a particle. Is it correct to say from the graph 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.