## An artificial satellite is moving in a circular orbit of radius

[question] Question. An artificial satellite is moving in a circular orbit of radius 42250 km. Calculate its speed if it takes 24 hours to revolve around the earth. [/question] [solution] Solution: Distance covered by the satellite in 24 hours. $S=2 \pi r$ $=2 \times \frac{22}{7} \times 42250$ $=265571.43 \mathrm{~km}$ Therefore speed of satellite $v=\frac{\text { distance travelled }}{\text { time taken }}=\frac{265571.43}{24 \times 60 \times 60}=3.07 \mathrm{kms}^{-1}$ [solution]...

## State which of the following situations

[question] Question. State which of the following situations are possible and give an example for each of these: (a) An object with a constant acceleration but with zero velocity. (b) An object moving in a certain direction with acceleration in the perpendicular direction. [/question] [solution] Solution: (a)A body with a constant acceleration but with zero velocity is possible. For example, when a body is just released, its initial velocity u = 0, but acceleration g = 10 ms–2 (b)It is possible ...

## The speed-time graph for a car is shown in figure below.

[question] Question. The speed-time graph for a car is shown in figure below. (a) Shade the area on the graph that represents the distance travelled by the car during the first 4 seconds. (b) Which part of the graph represents uniform motion of the car ? [/question] [solution] Solution: (a)During first 4 seconds, car is moving with non-uniform acceleration. Area of shaded portion represents distance travelled. (b)The straight line portion of the graph represents uniform motion of the car. [/solu...

## A ball is gently dropped from a height of 20 m.

[question] Question. A ball is gently dropped from a height of 20 m. If its velocity increases uniformly at the rate of 10 ms–2, with what velocity will it strike the ground? After what time will it strike the ground ? [/question] [solution] Solution: Given, initial velocity of ball, $\mathrm{u}=0$ Final velocity of ball, $\mathrm{v}=?$ Distance through which the ball falls, $\mathrm{s}=20 \mathrm{~m}$ Acceleration $\mathrm{a}=10 \mathrm{~ms}^{-2}$ Time of fall, $\mathrm{t}=$ ? We know $v^{2}-u^...

## Figure below shows the distance-time graph of three objects

[question] Question. Figure below shows the distance-time graph of three objects A, B and C. Study the graph and answer the following questions : (a) Which of the three is travelling the fastest ? (b)Are all three ever at the same point on the road? (c) How far has C travelled when B passes A ? (d) How far has B travelled by the time it passes C ? [question] [solution] Solution: (a) Car B is travelling the fastest, because its slope is largest among the three. (b) No, they are never at the same ...

## The driver of a car travelling at 52 km h–1 applies the brakes and accelerates uniformly in the opposite direction.

[question] Question. The driver of a car travelling at 52 km h–1 applies the brakes and accelerates uniformly in the opposite direction. The car stops in 5 s. Another driver going at 3 kmh–1 in another car, applies his brakes slowly and stops in 10 s. On the same graph paper, plot the speed versus time graphs for the two cars. Which of the two cars travelled farther after the brakes were applied ? [/question] [solution] Solution: The speed time graph of both the cars are shown below. (i) Distanc...

## A motorboat starting from rest on a lake accelerates in a straight line at a constant rate of 3.0 ms–2 for 8.0 s.

[question] Question. A motorboat starting from rest on a lake accelerates in a straight line at a constant rate of 3.0 ms–2 for 8.0 s. How far does the boat travel during this time ? [/question] [solution] Solution: Given, initial velocity of boat, u = 0 Acceleration, $\mathrm{a}=3.0 \mathrm{~m} \mathrm{~s}^{-2}$ Time, $\mathrm{t}=8 \mathrm{~s}$ Distance covered, $\mathrm{s}=$ ? Using the relation $\mathrm{s}=\mathrm{ut}+\frac{1}{2} \mathrm{at}^{2}$ we have, $\mathrm{s}=0 \times 8+\frac{1}{2} \t...

## Abdul while driving to school computes the average speed for his trip to be 20 km h–1.

[question] Question. Abdul while driving to school computes the average speed for his trip to be 20 km h–1. On his return trip along the same route, there is less traffic and the average speed is 40 km h–1. What is the average speed for Abdul's trip ? [/question] [solution] Solution: Let one way distance for his trip be S. Let $t_{1}$ be the time for his trip from home to school and $t_{2}$ be the time for his return trip. Then $\mathrm{t}_{1}=\frac{\mathrm{S}}{\mathrm{v}_{1}}=\frac{\mathrm{S}}{...

## Joseph jogs from one end A to the other end B of a straight

[question] Question. Joseph jogs from one end A to the other end B of a straight 300 m road in 2 minutes 50 seconds and then turns around and jogs 100 m back to point C in another 1 minute. What are Joseph's average speeds and velocities in jogging (a) from A to B and (b) from A to C ? [/question] [solution] Solution: The required figure is as shown (a) Distance covered = 300 m Time taken $=2 \mathrm{~min}$ and $50 \mathrm{~s}=170 \mathrm{~s}$ Now average speed from $A$ to $B$ is given by $\math...

## An athlete completes one round of a circular track of diameter 200 m in 40 s.

[question] Question. An athlete completes one round of a circular track of diameter 200 m in 40 s. What will be the distance covered and the displacement at the end of 2 minutes 20 s ? [/question] [solution] Solution: Given Diameter of circular track, $2 \mathrm{r}=200 \mathrm{~m}$ Circumference of circular track $=2 \pi \mathrm{r}$ $s=\pi(2 r)=\frac{22}{7} \times 200=\frac{4400}{7} \mathrm{~m}$ Time for completing one round $=40 \mathrm{~s}$. Time for which the athlete ran $=2 \mathrm{~min}$ an...

## A stone is thrown in vertically upward direction with a velocity of 5 ms–1.

[question] Question. A stone is thrown in vertically upward direction with a velocity of 5 ms–1. If the acceleration of the stone during its motion is 10 ms–2 in the downward direction, what will be the height attained by the stone and how much time will it take to reach there? [/question] [solution] Solution: Given, initial velocity, $\mathrm{u}=5 \mathrm{~ms}^{-1}$ Final velocity, $\mathrm{v}=0$ Since, $\mathrm{u}$ is upward \& a is downward, it is a retarded motion. $\therefore \mathrm{a}=-10...

## A racing car has uniform acceleration of 4 ms–2.

[question] Question. A racing car has uniform acceleration of 4 ms–2. What distance will it cover in 10 s after start ? [/question] [solution] Solution: Given Initial velocity, $\mathrm{u}=0$ Acceleration, $a=4 \mathrm{~ms}^{-2}$ Time, $\mathrm{t}=10 \mathrm{~s}$ Distance covered, $\mathrm{s}=?$ We know, s $=$ ut $+\frac{1}{2} \mathrm{at}^{2}$ $\mathrm{s}=0 \times 10+\frac{1}{2} \times 4 \times(10)^{2}$ $=0+200=200 \mathrm{~m}$ Therefore, distance covered $=200 \mathrm{~m}$. [/solution]...

## A trolley, while going down an inclined plane,

[question] Question. A trolley, while going down an inclined plane, has an acceleration of 2 cms–2. What will be its velocity 3 s after the start ? [/question] [solution] Solution: Given, initial velocity, $\mathrm{u}=0$; final velocity, $\mathrm{v}=?$ Time, $\mathrm{t}=3 \mathrm{~s}$ Acceleration, $\mathrm{a}=2 \mathrm{cms}^{-2}$ We know that, $\mathrm{v}=\mathrm{u}+\mathrm{at}$ or $\mathrm{v}=0+2 \times 3=6 \mathrm{cms}^{-1}$ Therefore, final velocity $=6 \mathrm{cms}^{-1}$. [/solution]...

## What is the quantity which is measured by

[question] Question. What is the quantity which is measured by the area occupied below the velocity-time graph ? [/question] [solution] Solution: Distance is the quantity which is measured by the area under velocity time graph. [/solution]...

## What can you say about the motion of an object if its speed-time graph

[question] Question. What can you say about the motion of an object if its speed-time graph is a straight line parallel to the time axis ? [/question] [solution] Solution: he object may be in uniform motion. [/solution]...

## What can you say about the motion

[question] Question. What can you say about the motion of an object whose distance time-graph is a straight line parallel to the time axis ? [question] [solution] Solution: The object is stationary. [solution]...

## What is the nature of the distance time graphs

[question] Question. What is the nature of the distance time graphs for uniform and non-uniform motion of an object? [question] [solution] Solution: The distance-time graph for uniform motion is a straight line, not parallel to the time axis. The distance-time graph for non-uniform motion is not a straight line, it can be a curve or a zigzag line [solution]...

## A bus decreases its speed from 80 km

[question] Question. A bus decreases its speed from 80 km h–1 to 60 km h–1 in 5 s. Find the acceleration of the bus. [question] [solution] Solution: Given $t=5 \mathrm{~s}$ Initial speed of bus $\mathrm{u}=80 \mathrm{~km} \mathrm{~h}^{-1}=80 \times \frac{5}{18}=22.2 \mathrm{~ms}^{-1}$ Final speed of the bus $\mathrm{v}=60 \mathrm{~km} \mathrm{~h}^{-1}=60 \times \frac{5}{18}=16.6 \mathrm{~ms}^{-1}$ Now acceleration is given by the relation $\mathrm{a}=\frac{\mathrm{v}-\mathrm{u}}{\mathrm{t}}=\fra...

## When will you say a body is in

[question] Question. When will you say a body is in (i) Uniform acceleration ? (ii) Non uniform acceleration ? [question] [solution] Solution: (i) A body is in uniform acceleration when it moves in a straight line and equal changes of velocity take place in equal intervals of time. (ii) A body is said to be possessing non-uniform acceleration when unequal changes in velocity take place in equal intervals of time....

## During an experiment a signal from a spaceship reached the ground station

[question] Question. During an experiment a signal from a spaceship reached the ground station in five minutes. What was the distance of the space ship from the ground station ? The signal travels at the speed of light that is, $3 \times 10^{8} \mathrm{~m} / \mathrm{s}$. [/question] [solution] Solution: Let the distance between the spaceship and the ground station be 's'. Then, $\mathrm{s}=\mathrm{v} \times \mathrm{t}$ where, $\mathrm{v}=$ speed of signal $=3 \times 10^{8} \mathrm{~m} / \mathrm{...

## What does the path of an object look like when it is in uniform motion ?

[question] Question. What does the path of an object look like when it is in uniform motion ? [/question] [solution] Solution: In uniform motion, the object moves along a straight path i.e. the path of object is a straight line. [/solution]...

## What does the odometer of an automobile measure?

[question] Question. What does the odometer of an automobile measure? [/question] [solution] Solution: Odometer measures the distance travelled by the automobile. [/solution]...

## Which of the following is true for displacement ?

[question] Question. Which of the following is true for displacement ? (a) It cannot be zero. (b) Its magnitude is greater than the distance travelled by the object. [/question] [solution] Solution: None of the statements (a) or (b) is true for displacement. [/solution]...

## Under what condition is the magnitude

[question] Question. Under what condition is the magnitude of average velocity of an object equal to its average speed ? [/question] [solution] Solution: When an object moves along a straight path without change in its direction, the average velocity of an object is equal to its average speed. [/solution]...

## Distinguish between speed and velocity.

[question] Question. Distinguish between speed and velocity. [solution] [question] Solution: Speed is rate of change of distance, while velocity is the rate of change of displacement. Speed is a scalar quantity, while velocity is a vector quantity. Speed is always positive, while velocity is positive, negative or zero. [solution]...

## A farmer moves along the boundary of a square field

[question] Question. A farmer moves along the boundary of a square field of side 10 m in 40 s. What will be the magnitude of displacement of the farmer at the end of 2 minutes 20 seconds ? [question] [solution] Solution: The perimeter of square field $\mathrm{ABCD}=4 \times 10 \mathrm{~m}=40 \mathrm{~m}$. Time for moving around the $10 \mathrm{~m}$ square field once $=40 \mathrm{~s}$. Time for journey of farmer $=2 \mathrm{~min}$ and $20 \mathrm{~s}=140 \mathrm{~s}$. Number of times the farmer m...

## An object has moved through a distance. Can it have zero displacement?

[question] Question. An object has moved through a distance. Can it have zero displacement? If yes, support your answer with an example. [/question] [solution] Solution: Yes, an object which has moved through a distance can have zero displacement. Example : When a person, walking along a circular path, returns back to the starting point, after completing a circle, his displacement is zero. But he covers a distance 2r, where 'r' is the radius of circular path. [/solution]...