Displacement includes direction as well as magnitude and is thus a vector. Speed, distance and time are scalars.

Total distance = 4 + 3 = 7 m. Net displacement = 4 east − 3 west = 1 m east (final relative to start).

Instantaneous velocity is the instantaneous rate of change of displacement — graphically the slope of the tangent to displacement–time graph at that instant.

Acceleration is change in velocity (magnitude or direction). Color change is unrelated to motion.

Acceleration is the rate of change of velocity. If velocity doesn't change, acceleration is zero.

Acceleration measures change in velocity per unit time — metres per second squared (m/s²).

Divide by 3.6: 54 ÷ 3.6 = 15 m/s (or multiply by 5/18).

Metre (m) is a unit of distance, not speed (speed requires distance per unit time).

36 ÷ 3.6 = 10 m/s.

This relates initial velocity u, final velocity v, acceleration a and time t for uniform acceleration.

With u = 0, s = ut + ½at² reduces to s = ½at².

This equation links u, v, a and s without time t — useful when time is not given.

a = (v − u)/t = (25 − 5)/10 = 20/10 = 2 m/s².

v = u + at = 0 + 5×4 = 20 m/s.

s = ut + ½at² = 0 + 0.5×3×16 = 24 m.

Set v=0 and a=−g: 0 = u² − 2gH → H = u²/(2g).

Slope (Δs/Δt) of displacement–time graph gives velocity. For distance graph, slope gives speed.

Area under velocity–time graph (velocity × time) gives displacement over that period.

Horizontal v–t line means velocity is constant (acceleration zero).

Average velocity = displacement / time = 12 m / 4 s = 3 m/s.

Near Earth's surface g ≈ 9.8 m/s² (often approximated as 10 m/s² in simple problems).

From v = u + at with u=0 and a=g, v = gt (magnitude downward).

Even at top where velocity is momentarily zero, acceleration due to gravity remains downward (≈ g); it doesn't become zero.

s = ½ g t² → 19.6 = 0.5×9.8×t² → t² = 4 → t = 2 s.

Relative velocity of A w.r.t B is vector subtraction vA − vB (how A appears to move as seen from B).

When moving towards each other along a line, relative (closing) speed = sum of magnitudes = 4 + 6 = 10 m/s.

Upstream speed = speed in still water − current = 8 − 3 = 5 km/h.

v = u + at = 0 + 2×8 = 16 m/s.

a = (0−25)/5 = −5 m/s². s = ut + ½at² = 25×5 + 0.5×(−5)×25 = 125 − 62.5 = 62.5 m.

State sign convention (which direction is positive), convert quantities to SI (m, s), and pick the kinematic equation containing the given quantities — this avoids common mistakes.