Lesson 9 of 9 · 15 min
Chapter review
Watch a class
The whole chapter on YouTube
Must-know facts
16 facts
- 01Displacement can be positive, negative or zero; distance (path length) is always positive or zero.
- 02Magnitude of displacement ≤ distance, with equality only when the body moves in one direction without turning back.
- 03Average speed equals the magnitude of average velocity only if the direction of motion never reverses.
- 04Slope of the x-t graph = velocity; slope of the v-t graph = acceleration; area under the v-t graph = displacement.
- 05At the top of a vertical throw, v = 0 but a = g downward.
- 06v = v₀ + at, x = v₀t + ½at², v² = v₀² + 2ax hold only for constant acceleration.
- 07km/h × 5/18 = m/s; for example 72 km/h = 20 m/s and 54 km/h = 15 m/s.
- 08Maximum height of a body thrown up with speed u is u²/2g, reached in time u/g.
- 09Time of ascent equals time of descent to the same level when air resistance is neglected.
- 10Distances in successive equal time intervals from rest: 1 : 3 : 5 : 7 (Galileo's law of odd numbers).
- 11Distances covered from rest in times t, 2t, 3t are in the ratio 1 : 4 : 9.
- 12Stopping distance varies as the square of initial speed.
- 13Reaction time from a dropped ruler: t = √(2d/g).
- 14Free-fall acceleration does not depend on the mass of the body (air resistance neglected).
- 15Uniform motion: straight x-t line and a v-t line parallel to the time axis.
- 16Speeding up means v and a have the same sign; slowing down means they have opposite signs.
Common traps
Where marks are lost
Formulas
13 to know
Average velocity
v̄ = Δx/Δt = (x₂ − x₁)/(t₂ − t₁)
Displacement over time; sign follows the chosen positive direction.
Average speed
average speed = total path length / total time
Never negative.
Instantaneous velocity
v = dx/dt
Slope of the tangent to the x-t graph.
Instantaneous acceleration
a = dv/dt = d²x/dt²
Slope of the v-t graph; unit m s⁻².
Velocity-time relation
v = v₀ + at
Constant acceleration only.
Position-time relation
x = v₀t + ½at²
x is displacement from the position at t = 0.
Velocity-position relation
v² = v₀² + 2ax
Constant acceleration; x is displacement.
Displacement with average velocity
x = (v₀ + v)t/2
Constant acceleration only.
Free fall from rest
y = ½gt², v = gt, v² = 2gy
y measured downward from the release point, g ≈ 9.8 m s⁻².
Maximum height of a vertical throw
H = u²/2g, time to top = u/g
Air resistance neglected.
Stopping distance
d = v₀²/2a
a is the magnitude of the constant retardation.
Reaction time from a falling ruler
t = √(2d/g)
d is the distance the ruler falls before it is caught.
Displacement in the nth second
sₙ = v₀ + a(2n − 1)/2
Derived from x = v₀t + ½at² as x(n) − x(n − 1), with t in seconds; constant acceleration, no reversal of direction within that second. A derived result, not an equation NCERT lists.
Key terms
12 terms
- Point object
- A body whose size can be ignored because it is small compared with the distance it moves.
- Displacement
- The change in position, with sign; depends only on where the motion starts and ends.
- Path length
- The total length of the route actually covered; always non-negative.
- Average velocity
- Displacement divided by the time interval in which it occurs.
- Instantaneous velocity
- The rate of change of position at a particular instant, dx/dt.
- Speed
- The magnitude of velocity at an instant; average speed is path length over time.
- Acceleration
- How fast velocity changes with time, dv/dt.
- Uniform motion
- Motion with constant velocity, so equal displacements in equal time intervals.
- Uniformly accelerated motion
- Motion in which velocity changes by equal amounts in equal time intervals.
- Free fall
- Motion under gravity alone, with air resistance neglected, at acceleration g downward.
- Stopping distance
- The distance a moving vehicle covers after the brakes are applied until it comes to rest.
- Reaction time
- The time a person takes to respond after noticing something.