Describing Motion Around Us

Flashcards covering key definitions, formulas, graphical interpretations, and examples from Chapter 4: Describing Motion Around Us.

When is an object said to be in motion with respect to a reference point?

An object is said to be in motion if its position with respect to a reference point changes with time. If its position with respect to the reference point does not change with time, the object is said to be at rest.

How do scalar quantities differ from vector quantities?

Physical quantities that can be specified by just their numerical value (magnitude with units) are called scalars. Physical quantities that require specifying both direction and magnitude are called vectors.

What is displacement, and what information is needed to describe it completely?

Displacement is the net change in the position of an object between two given instants of time. Describing it requires specifying its magnitude (the distance between positions at two instants) and its direction (from the position at the first instant towards the position at the second instant).

Under what condition are the total distance travelled and the magnitude of displacement equal for motion in a straight line?

They are equal if the object moves without turning back, that is, if it moves in one direction only.

Which ancient Indian scientific texts are referenced regarding the concept that speed is distance divided by time?

The treatise Aryabhatiya (5th century CE) and the comprehensive mathematical text Ganitakaumudi (14th century CE).

How is average speed defined, and what is its formula?

Average speed is the total distance travelled divided by the time interval during which this distance is covered: $\text{average speed} = \frac{\text{total distance travelled}}{\text{time interval}}$.

How is average velocity defined, and how is it expressed in formula form using displacement $s$ and time interval $t$?

Average velocity is the change in position (displacement) divided by the time interval in which it occurs: $v_{av} = \frac{s}{t}$. It represents the average rate of change of position of an object with respect to time.

In Example 4.2, what are Sarang's average speed and average velocity if he swims across a $25\,m$ pool and returns to the starting point in $50\,s$?

His average speed is $\frac{50\,m}{50\,s} = 1\,m\,s^{-1}$, and his average velocity is $\frac{0\,m}{50\,s} = 0\,m\,s^{-1}$.

What is instantaneous velocity?

Instantaneous velocity is the velocity of an object at a particular instant of time, which is reached as the time interval around that instant becomes infinitesimally small.

What is average acceleration, and what formula defines it when velocity changes from $u$ at time $t_1$ to $v$ at time $t_2$?

Average acceleration is the change in velocity divided by the time interval: $a = \frac{v - u}{t_2 - t_1}$. Its SI unit is $m\,s^{-2}$ (or $m/s^2$).

For straight-line motion, what is the direction of average acceleration when a vehicle speeds up versus when it slows down?

When the magnitude of velocity is increasing (speeding up), average acceleration is in the direction of velocity. When the magnitude of velocity is decreasing (slowing down), average acceleration acts opposite to the direction of velocity.

Can an object have a high velocity and yet have zero acceleration?

Yes. Acceleration depends on how quickly velocity is changing, not on how fast an object moves. For example, a bus moving along a straight highway at a constant velocity has zero acceleration.

What is the value and nature of the average acceleration for an object dropped vertically from a height in Example 4.4?

The average acceleration is constant across every successive $1\,s$ interval and equals $9.8\,m\,s^{-2}$, directed downwards in the direction of motion (acceleration due to gravity, denoted by $g$).

What physical quantity is represented by the slope of a position-time graph?

The slope of a position-time graph represents the velocity (or average velocity) of the object, which is the rate of change of position with respect to time.

What does a straight horizontal line parallel to the time axis on a position-time graph indicate?

It indicates that the position of the object is not changing with time, meaning the object is stationary (at rest).

Which two physical quantities can be calculated from a velocity-time graph?

The slope of the line on a velocity-time graph gives the acceleration, and the area enclosed between the line on the graph and the time axis gives the displacement.

What are the three kinematic equations for motion in a straight line with constant acceleration?

1. $v = u + at$\n2. $s = ut + \frac{1}{2}at^2$\n3. $v^2 = u^2 + 2as$, where $u$ is initial velocity, $v$ is final velocity, $a$ is constant acceleration, $t$ is time interval, and $s$ is displacement.

According to Example 4.8, what is the stopping distance of a car when brakes produce an acceleration of $-4\,m\,s^{-2}$ from initial velocities of (i) $54\,km\,h^{-1}$ and (ii) $108\,km\,h^{-1}$?

(i) $28.1\,m$ (using $u = 15\,m\,s^{-1}$)\n(ii) $112.5\,m$ (using $u = 30\,m\,s^{-1}$).

What is uniform circular motion, and why is it considered an accelerated motion?

Uniform circular motion is the motion of an object along a circular path with constant (uniform) speed. It is an accelerated motion because the direction of velocity continuously changes at every point along the path.

What is the formula for the average speed $v_{av}$ of an object completing one revolution of radius $R$ in time $T$ in uniform circular motion?

The formula is $v_{av} = \frac{2\pi R}{T}$. The average velocity over this same complete revolution is $0$ because the net displacement is $0$.