Motion, vectors and projectiles flashcards

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Scalar quantity
A quantity with magnitude only (e.g. speed, mass, energy).
Vector quantity
A quantity with both magnitude and direction (e.g. displacement, velocity, force).
Displacement
Distance in a stated direction from the starting point. A vector, unit m.
Velocity
Rate of change of displacement. A vector, unit m s⁻¹.
Acceleration
Rate of change of velocity. A vector, unit m s⁻².
Resultant vector
The single vector that has the same effect as two or more vectors combined.
Projectile
A body moving freely under gravity alone after being launched (air resistance negligible).
Uniform acceleration
Acceleration that is constant in both magnitude and direction.
The four equations of uniformly accelerated motion
v = u + at · s = ½(u + v)t · s = ut + ½at² · v² = u² + 2as (Yes)
Components of a vector F at angle θ to the horizontal
Horizontal F cos θ; vertical F sin θ. (No — learn it)
Magnitude and direction of the resultant of perpendicular vectors A and B
R = √(A² + B²); angle to A = tan⁻¹(B/A). (No — learn it)
Fall from rest through height h in time t
h = ½gt² (s = ut + ½at² with u = 0). (No — derive it)
Time to the highest point for launch speed u at angle θ
t = u sin θ / g (vertical velocity becomes zero). (No — derive it)
Gradient of a displacement–time graph
Velocity (the gradient of the tangent gives instantaneous velocity).
Gradient of a velocity–time graph
Acceleration.
Area under a velocity–time graph
Displacement. Areas below the time axis count as negative displacement.
Area under an acceleration–time graph
Change in velocity.
Shape of the s–t graph for uniform acceleration from rest
A curve of steadily increasing gradient (a parabola through the origin).
What does a curved velocity–time graph tell you?
The acceleration is not uniform; find it from the gradient of a tangent, and the displacement from the area by counting squares.
Core Practical 1: which graph gives g, and how?
Plot h against t²; it is a straight line through the origin with gradient g/2, so g = 2 × gradient.
Why are the horizontal and vertical motions of a projectile independent?
Gravity acts only vertically, so the horizontal velocity stays constant while the vertical velocity changes at g.
Velocity and acceleration of a projectile at its highest point
Velocity: horizontal only, equal to u cos θ. Acceleration: g = 9.81 m s⁻² downwards.
When can you add two vectors by Pythagoras?
Only when they are at right angles. At other angles use a scale drawing or add components.
When can the equations of motion be used?
Only for constant acceleration in a straight line.
Core Practical 1: why use an electronic timer?
Human reaction time (about 0.2 s) is comparable to fall times of 0.2–0.5 s.
Core Practical 1: effect of measuring h from the top of the ball
Every h is too large by the ball's diameter: the line shifts (intercept) but the gradient, and so g, is unchanged.
A boat moves at 9.0 m s⁻¹ east and is pushed 4.0 m s⁻¹ north by a current. Resultant velocity?
√(9.0² + 4.0²) = 9.8 m s⁻¹ at tan⁻¹(4.0/9.0) = 24° north of east.
Resolve 120 N acting at 40° above the horizontal.
Horizontal 120 cos 40° = 92 N; vertical 120 sin 40° = 77 N.
A car speeds up uniformly from 5.0 to 25 m s⁻¹ over 150 m. Acceleration?
v² = u² + 2as → a = (625 − 25)/300 = 2.0 m s⁻². (Yes)
A ball leaves a 2.0 m high ledge horizontally at 12 m s⁻¹. How far does it travel horizontally?
t = √(2 × 2.0 / 9.81) = 0.64 s; distance = 12 × 0.639 = 7.7 m.
v–t graph: 0 → 10 m s⁻¹ uniformly in 4.0 s, then constant for 6.0 s. Distance?
Area = ½ × 4.0 × 10 + 6.0 × 10 = 80 m.
A ball is kicked at 15 m s⁻¹ at 30° from level ground. Time of flight?
u_V = 15 sin 30° = 7.5 m s⁻¹; time up = 7.5/9.81 = 0.76 s; total 1.5 s.
Vector answer with no direction
Incomplete. Give a sign with the positive direction stated, an angle from a named reference, or a compass direction.
Angle given from the vertical
The vertical component is F cos θ and the horizontal component is F sin θ — the roles swap.
A body below its launch point (upwards positive)
Its displacement is negative: s = −h. Getting this sign wrong spoils every later step.
“Show that” questions
Show every step and give the answer to one more significant figure than the value quoted.
Finding a gradient from a graph
Use a triangle covering at least half of the line and read its corners from the line, not from data points.
Which value of g?
Use 9.81 m s⁻² from the data list, not 10 m s⁻².

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