Correct option: (B).

Motion is identified by comparing the position of an object with respect to a chosen reference point at different instants of time.

Correct option: (C).

Position specifies how far an object is from a reference point and in which direction it lies.

Correct option: (B) Displacement.

Displacement is the net change in position between two specified instants and includes direction.

Correct option: (D) 160 m.

Distance depends on the complete path travelled.

Correct option: (A) 40 m.

Correct option: (D).

The magnitude of displacement is always less than or equal to the total distance travelled.

Correct option: (B).

When motion occurs along one straight direction without reversal, the actual path length equals the separation between initial and final positions.

Correct option: (B).

Correct option: (B).

Correct option: (B).

The swimmer covers a non-zero distance but has zero displacement after returning to the starting point.

Correct option: (A).

Equal distances in equal intervals, for all possible equal intervals, indicate constant speed in straight-line uniform motion.

Correct option: (B) m/s.

Correct option: (A).

Correct option: (A).

Acceleration depends on change in velocity, not on the magnitude of velocity alone.

Correct option: (B).

When the magnitude of velocity decreases, acceleration acts opposite to the direction of velocity.

Correct option: (B) 9.8 m/s².

This is denoted by g.

Correct option: (B).

The slope of a position-time graph represents velocity. A constant slope means constant velocity.

Correct option: (B).

The position does not change with time, so velocity is zero.

Correct option: (B) Acceleration.

Correct option: (B).

Correct option: (A).

Correct option: (A).

Correct option: (C).

Correct option: (C) Four times.

Therefore doubling speed makes the braking distance four times as large when braking acceleration is unchanged.

Correct option: (B).

Motion requiring two independent directions is motion in two dimensions or motion in a plane.

Correct option: (D) 2πR.

Correct option: (D) Zero.

The final position coincides with the initial position.

Correct option: (B).

Velocity includes direction. The direction changes continuously around the circle even though speed remains constant.

Correct option: (B).

The chapter describes velocity at any point of circular motion as lying along the tangent in the direction of motion.

Correct option: (C).

Acceleration occurs whenever velocity changes. A change in direction alone is sufficient to change velocity.

An object is at rest if its position relative to a selected reference point does not change with time. It is in motion if that relative position changes with time.

Distance is the total path length travelled and requires only a magnitude. Displacement is the net change between initial and final position and requires magnitude and direction.

For straight-line motion, the two are equal when the object moves only in one direction and does not turn back.

An instant is one particular clock reading. A time interval is the duration between two clock readings or two instants.

Average speed has no directional information, while average velocity has direction.

An object is in uniform straight-line motion when it travels equal distances in equal intervals of time for all possible choices of equal intervals. Its speed is constant.

Average acceleration is change in velocity divided by the corresponding time interval.

Yes. An object moving along a straight line with constant velocity has zero acceleration because its velocity is not changing, regardless of how large that velocity is.

The slope represents the rate at which position changes with time and therefore gives velocity for a straight-line graph.

The slope gives acceleration, while the area between the graph and time axis gives displacement for the cases considered in the chapter.

They apply to straight-line motion with constant acceleration.

Signs indicate direction. Changing the chosen positive direction midway would change the meaning of positive and negative quantities and lead to inconsistent equations and incorrect conclusions.

Uniform circular motion is motion along a circular path with constant speed. Although speed remains constant, the direction of velocity changes continuously.

The object returns to its original position, so displacement is zero. Since average velocity = displacement/time, average velocity for the complete revolution is zero.

Distance records the entire path, while displacement connects initial and final positions with direction.

Total distance = 400 km.

Total time = 5 h.

Since the person returns to the initial position, displacement = 0.

The negative sign indicates that acceleration acts opposite to the chosen positive direction of motion while the vehicle slows down.

u = 28 m/s, v = 0, s = 98 m.

The slope of a position-time graph gives velocity. Since graph B has the greater slope, object B has the greater velocity. It covers a larger displacement during the same time interval.

Horizontal velocity-time line → velocity is constant.

Using the area of the velocity-time trapezium:

• A straight line with constant slope indicates constant velocity.
• A curved graph indicates that slope changes with time.
• Changing slope means changing velocity and hence accelerated motion.

• Velocity increases by equal amounts in equal intervals.
• The graph is a straight line sloping upward.
• The constant slope represents constant positive acceleration.

54 km/h = 15 m/s and 36 km/h = 10 m/s.

For constant acceleration:

• Speed remains constant throughout the lap.
• Average velocity for one complete lap is zero because displacement is zero.
• Instantaneous velocity is non-zero and continuously changes direction, remaining tangent to the circular path.

The person travels the 250 m route four times:

Final position = initial position.

This demonstrates that a large distance can correspond to zero displacement.

Ground to fourth floor:

Fourth to second floor:

Total distance:

Final position is second floor, 6 m above the starting position.

Convert velocities:

Acceleration stage:

Braking stage:

The negative sign indicates acceleration opposite to the initial direction of velocity.

• Horizontal line: slope = 0, so position is unchanged and object is at rest.
• Straight inclined line: constant slope, so velocity is constant.
• Curved line: slope changes with time, so velocity changes and motion is accelerated.

A steeper straight line represents a larger magnitude of velocity.

• The vertical coordinate gives velocity at any chosen instant.
• The slope gives acceleration.
• A horizontal line means zero acceleration.
• The area between the graph and time axis gives displacement over the selected time interval.

For constant acceleration:

Multiplying by t:

Rearranging:

This relates final velocity to initial velocity, acceleration and elapsed time.

For constant acceleration, displacement equals area under the velocity-time graph.

The area consists of a rectangle and triangle:

Using:

we obtain:

54 km/h = 15 m/s.

108 km/h = 30 m/s.

Doubling the speed has increased braking distance by a factor of four.

Stage 1:

Stage 2:

Stage 3:

36 km/h = 10 m/s.

Reaction distance:

Braking distance:

Total stopping distance:

The obstacle is 30 m away, so the bus stops approximately 5 m before it.

There are at least two components of stopping distance:

• Reaction distance: approximately proportional to speed for a fixed driver reaction time.
• Braking distance: for fixed braking acceleration, it follows from v² = u² + 2as that stopping distance is proportional to the square of initial speed.

Road conditions, tyres and braking capacity can further increase the distance needed.

First 2 min = 120 s:

Accelerated part:

The object moves throughout the interval but ends where it started.

Half the circumference:

Initial and final points are opposite ends of a diameter:

Since πR > 2R, distance exceeds displacement.

• Velocity depends on both speed and direction.
• In uniform circular motion, speed is constant.
• However, the direction of velocity changes continuously.
• Therefore velocity changes continuously and acceleration is non-zero.

The instantaneous velocity at each point is tangent to the circular path.

The student returns to the starting position despite travelling 200 m.

Yes.

Journey A: 50 m east → distance = 50 m, displacement = 50 m east.

Journey B: 80 m east followed by 30 m west → distance = 110 m, displacement = 50 m east.

Therefore displacement depends only on initial and final positions, while distance depends on the entire path.

No. Zero displacement only means the final position equals the initial position.

The object could travel a considerable path and return.

Therefore:

Both cover the same total distance in the same total time.

Therefore both have the same average speed even though their instantaneous speeds may differ.

Let each time interval be t.

No. Equal distances do not correspond to equal times.

Let each distance be 60 m.

Take east as positive.

The magnitudes are equal, but directions are opposite.

The negative sign reflects the chosen direction and the reversal of velocity.

The intersection means both objects occupy the same position at the same instant.

The steeper graph has greater slope and hence a greater velocity magnitude.

The crossing does not mean their velocities are equal.

Yes. Two position-time graphs may intersect at one point, indicating the same position and time. If the slopes of the graphs at that point differ, their velocities differ.

Thus equality of position does not imply equality of velocity.

Slope:

Area:

First find final velocity:

Method 1:

Method 2:

For constant acceleration, the area under the velocity-time graph forms a trapezium with parallel sides u and v and height t.

Since the area represents displacement:

From:

we get:

Substitute in:

The derivations assume acceleration is constant throughout the interval. Under that assumption, velocity changes linearly with time and the velocity-time graph is a straight line.

If acceleration changes unpredictably, the same simple relationships among u, v, a, s and t no longer describe the entire interval.

For constant braking magnitude:

Hence:

The faster car requires nine times the braking distance.

Reaction distance = speed × reaction time, so doubling speed doubles reaction distance.

With unchanged braking acceleration:

Therefore braking distance becomes approximately four times as large.

Quarter circumference:

Initial and final radii are perpendicular. The displacement is the chord:

Distance:

After one full revolution it returns to the start. The extra half revolution takes it to the opposite point.

This is half a revolution.

No.

They complete revolutions in the same period T, but:

The point at 7 cm covers a larger circumference in the same time and therefore has greater linear speed.

Yes.

A speedometer mainly indicates the magnitude of velocity. Around the circular path, this magnitude may remain constant while the direction of velocity changes continuously.

Since velocity changes, acceleration is non-zero.

While constrained to the circle, the marble’s velocity at each instant is directed along the tangent to the circle.

When the ring is removed, the constraint maintaining the circular path disappears. At that instant, the marble continues in the direction of its instantaneous velocity—along the tangent.

The statement is true only in a restricted situation.

Straight-line constant-velocity motion: If both speed and direction remain unchanged, velocity is constant and acceleration is zero.

Uniform circular motion: Speed remains constant, but the direction of velocity changes at every point. Therefore velocity is continuously changing.

Thus constant speed alone is insufficient to conclude that acceleration is zero.