Kinematics flash cards

1. 1.What is the difference between distance and displacement?

   Distance is the total path length travelled (scalar, always positive). Displacement is the shortest straight-line vector from initial to final position (has magnitude and direction, can be zero or negative).

   Hint: One is path length, the other is a straight-line vector.

2. 2.For any journey, how do the magnitudes of distance and displacement compare?

   Distance $\geq$ magnitude of displacement. They are equal only when the motion is along a straight line without any change in direction.

   Hint: Path length is never less than the straight-line separation.

3. 3.A body completes one full circle of radius $r$. Find its distance and displacement.

   Distance $= 2\pi r$ (full circumference). Displacement $= 0$, since it returns to the starting point.

   Hint: Start point equals end point for a full loop.

4. 4.Define average speed and average velocity.

   Average speed $= \dfrac{\text{total distance}}{\text{total time}}$ (scalar). Average velocity $= \dfrac{\text{displacement}}{\text{total time}}$ (vector).

   Hint: Speed uses distance; velocity uses displacement.

5. 5.When can average speed and the magnitude of average velocity be equal?

   When the body moves in a straight line in a single direction (no reversal), so distance equals displacement magnitude.

   Hint: No change of direction along the path.

6. 6.Define instantaneous velocity.

   The velocity at a particular instant: $v = \dfrac{dx}{dt}$, the limit of average velocity as the time interval $\to 0$. It equals the slope of the $x$–$t$ graph at that instant.

   Hint: Derivative of position with respect to time.

7. 7.Define instantaneous speed and how it relates to instantaneous velocity.

   Instantaneous speed is the magnitude of instantaneous velocity. Unlike average values, instantaneous speed always equals the magnitude of instantaneous velocity.

   Hint: At an instant, speed = |velocity| exactly.

8. 8.Define acceleration and give its SI unit.

   Acceleration is the rate of change of velocity: $a = \dfrac{dv}{dt}$. It is a vector. SI unit: $\text{m s}^{-2}$.

   Hint: How fast velocity changes.

9. 9.What does negative acceleration (retardation) mean?

   Acceleration acting opposite to the direction of velocity, which decreases the speed. Note: negative acceleration does not always mean slowing down — it depends on the direction chosen as positive.

   Hint: Opposite to velocity means deceleration.

10. 10.Can a body have zero velocity but non-zero acceleration? Give an example.

    Yes. At the highest point of a vertical throw, velocity is momentarily zero but acceleration $= g$ downward.

    Hint: Think of the top of a vertical throw.

11. 11.Can a body have constant speed but changing velocity?

    Yes. In uniform circular motion, speed is constant but the direction of velocity changes continuously, so velocity (a vector) changes and there is acceleration.

    Hint: Circular motion at steady rate.

12. 12.State the three equations of motion for uniform acceleration.

    $v = u + at$; $\quad s = ut + \tfrac{1}{2}at^2$; $\quad v^2 = u^2 + 2as$, where $u$ = initial velocity, $v$ = final velocity, $a$ = acceleration, $s$ = displacement.

    Hint: v-u-a-t, then s, then v-squared.

13. 13.Under what condition are the equations of motion ($v=u+at$, etc.) valid?

    Only when acceleration is constant (uniform) in both magnitude and direction, and motion is along a straight line.

    Hint: They require uniform acceleration.

14. 14.Give the formula for displacement in the $n$th second of uniformly accelerated motion.

    $s_{n} = u + \dfrac{a}{2}(2n - 1)$. This gives the distance covered during the $n$th second only, not in $n$ seconds.

    Hint: Uses $(2n-1)$; it is a distance-per-second, not total.

15. 15.For a body starting from rest under uniform acceleration, in what ratio are distances covered in successive equal time intervals?

    $1 : 3 : 5 : 7 : \ldots$ (ratio of odd numbers), known as Galileo's odd-number rule.

    Hint: Odd numbers.

16. 16.For a body starting from rest under uniform acceleration, how do total distances after $1,2,3\ldots$ seconds compare?

    They are in the ratio $1 : 4 : 9 : 16 : \ldots$ (squares of natural numbers), since $s \propto t^2$.

    Hint: Perfect squares.

17. 17.What is the acceleration due to gravity $g$ and its standard value?

    $g$ is the acceleration of a freely falling body near Earth's surface, directed downward, with standard value $g \approx 9.8\ \text{m s}^{-2}$ (often taken as $9.8$ or $10$).

    Hint: About $9.8\ \text{m s}^{-2}$ downward.

18. 18.How are the equations of motion written for a body dropped from rest (free fall)?

    With $u=0$, taking downward positive: $v = gt$, $\; h = \tfrac{1}{2}gt^2$, $\; v^2 = 2gh$.

    Hint: Replace $a$ with $g$ and $u=0$.

19. 19.For a body thrown vertically upward with speed $u$, what are the time to reach the top and the maximum height?

    Time to top $t = \dfrac{u}{g}$; maximum height $H = \dfrac{u^2}{2g}$ (velocity is zero at the top).

    Hint: At top, $v=0$.

20. 20.For vertical projection, how does time of ascent compare with time of descent?

    They are equal (in the absence of air resistance): $t_{up} = t_{down} = \dfrac{u}{g}$. Total time of flight $= \dfrac{2u}{g}$.

    Hint: Up-time equals down-time.

21. 21.For a body thrown up with speed $u$, what is its speed when it returns to the point of projection?

    It returns with the same speed $u$ (magnitude), but directed downward. Speed at any height is the same going up as coming down.

    Hint: Same magnitude, opposite direction.

22. 22.On a position–time ($x$–$t$) graph, what does the slope represent?

    The slope of an $x$–$t$ graph gives the velocity. A steeper slope means greater speed; a horizontal line means the body is at rest.

    Hint: Slope of x–t is velocity.

23. 23.On a velocity–time ($v$–$t$) graph, what do the slope and the area represent?

    Slope of a $v$–$t$ graph gives acceleration; the area under the graph gives displacement.

    Hint: Slope = acceleration, area = displacement.

24. 24.What does a straight horizontal line on a $v$–$t$ graph indicate?

    Constant velocity (zero acceleration); the body moves uniformly. The area under it (a rectangle) gives the displacement.

    Hint: Flat line = uniform velocity.

25. 25.What kind of $x$–$t$ graph corresponds to uniformly accelerated motion from rest?

    A parabola (curve of increasing slope), because $x = \tfrac{1}{2}at^2$ is quadratic in $t$.

    Hint: Parabolic curve.

26. 26.What does the $x$–$t$ graph of a body at rest look like?

    A horizontal straight line parallel to the time axis (position does not change with time), so velocity = slope = 0.

    Hint: Flat line parallel to time axis.

27. 27.On a $v$–$t$ graph, how do you find total distance vs displacement when velocity changes sign?

    Displacement = signed (net) area, counting area below the time axis as negative. Distance = total unsigned area, adding magnitudes of areas above and below.

    Hint: Signed area vs total area.

28. 28.Define uniform motion and describe its $x$–$t$ graph.

    Motion with constant velocity (equal displacements in equal time intervals). Its $x$–$t$ graph is a straight line with constant, non-zero slope.

    Hint: Constant velocity, straight sloping line.

29. 29.Define relative velocity of object A with respect to object B.

    $\vec{v}_{AB} = \vec{v}_A - \vec{v}_B$: the velocity of A as observed from B's frame of reference.

    Hint: Subtract B's velocity from A's.

30. 30.Two bodies move along a straight line in the same direction with speeds $v_1$ and $v_2$. What is their relative velocity?

    Magnitude $= |v_1 - v_2|$ (the difference), directed along the faster body's motion.

    Hint: Same direction means subtract.

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