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Physics · Unit 2

Force and Motion: MDCAT Notes and MCQs

Kinematics

  • Displacement: shortest directed distance from initial to final position (vector). Average velocity = total displacement / total time.
  • Displacement–time graph: slope = velocity. Straight line = uniform velocity; curve = changing velocity; horizontal line = at rest.
  • Acceleration = Δv/Δt (m s−2). Uniform: equal velocity changes in equal intervals (straight v–t line); variable: otherwise. Area under v–t graph = displacement; slope = acceleration.
  • Equations: vf = vi + at; S = vit + ½at²; 2aS = vf² − vi².

Projectile motion (no air resistance)

  • Two-dimensional motion in a vertical plane. Horizontal velocity vx = v cos θ stays constant (ax = 0); vertical motion has ay = −g like free fall. Path = parabola.
  • Time of flight T = 2v sin θ / g. Maximum height H = v² sin²θ / 2g. Range R = v² sin 2θ / g.
  • Maximum range at θ = 45°: Rmax = v²/g (then H = Rmax/4).
  • Complementary angles (θ and 90° − θ, e.g. 30° and 60°) give the same range.
  • At the highest point: vertical velocity = 0, velocity = v cos θ (horizontal), acceleration still g downward.

Newton's laws & momentum

  • 1st law: inertia. 2nd law: F = Δp/Δt (rate of change of momentum) = ma when mass constant. 3rd law: action = reaction (on different bodies).
  • Momentum p = mv (kg m s−1 = N s). Impulse = FΔt = Δp.
  • Law of conservation of momentum (from the 3rd law): total momentum of an isolated system is constant. Applies to collisions and explosions (total momentum before = 0 → after = 0, fragments move in opposite directions; e.g. gun recoil mgvg = −mbvb).

Collisions (1-D)

  • Elastic: momentum and KE conserved. Inelastic: only momentum conserved (KE lost as heat, sound, deformation). Perfectly inelastic: bodies stick together.
  • Elastic: relative speed of approach = relative speed of separation (v1 − v2 = v2' − v1').
  • Equal masses, one at rest, elastic → they exchange velocities. Light body hitting very heavy body at rest → rebounds with same speed. Heavy hitting light → light moves at ≈ 2v.
PMDC learning outcomes for this unit
  • Kinematics, projectiles, Newton's laws, momentum: 2.1 Describe displacement.
  • Kinematics, projectiles, Newton's laws, momentum: 2.2 Describe average velocity of objects.
  • Kinematics, projectiles, Newton's laws, momentum: 2.3 Interpret displacement-time graph of objects moving along the same straight line.
  • Kinematics, projectiles, Newton's laws, momentum: 2.4 Describe acceleration
  • Kinematics, projectiles, Newton's laws, momentum: 2.5 Distinguish between uniform and variable acceleration.
  • Kinematics, projectiles, Newton's laws, momentum: 2.6 Explain that projectile motion is two-dimensional motion in a vertical plane.
  • Kinematics, projectiles, Newton's laws, momentum: 2.7 Communicate the ideas of a projectile in the absence of air resistance.
  • Kinematics, projectiles, Newton's laws, momentum: 2.8 Explain horizontal component (VH) of velocity is constant.
  • Kinematics, projectiles, Newton's laws, momentum: 2.9 Acceleration is in the vertical direction and is the same as that of a vertically free-falling object.
  • Kinematics, projectiles, Newton's laws, momentum: 2.10 Differentiate between the characteristics of horizontal motion and vertical motion
  • Kinematics, projectiles, Newton's laws, momentum: 2.11 Evaluate maximum height, range, time of flight, launch angle for maximum range and complementary angles giving the same range.
  • Kinematics, projectiles, Newton's laws, momentum: 2.12 Apply Newton's laws to explain the motion of objects in a variety of contexts.
  • Kinematics, projectiles, Newton's laws, momentum: 2.13 Describe Newton's second law of motion as rate of change of momentum.
  • Kinematics, projectiles, Newton's laws, momentum: 2.14 Correlate Newton's third law of motion and conservation of momentum.
  • Kinematics, projectiles, Newton's laws, momentum: 2.15 Solve problems of elastic and inelastic collisions in one dimension using conservation of momentum.
  • Kinematics, projectiles, Newton's laws, momentum: 2.16 Describe that momentum is conserved in all situations (e.g. explosions).
  • Kinematics, projectiles, Newton's laws, momentum: 2.17 Identify that for a perfectly elastic collision, relative speed of approach = relative speed of separation.

Force and Motion MCQs with answers

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Q1
The slope of a displacement–time graph represents:
AForce
BDistance
CVelocity
DAcceleration
Show answer
Answer: C (Velocity). Slope of s–t graph = Δs/Δt = velocity.
Q2
In projectile motion (no air resistance), the horizontal component of velocity:
ADecreases
BRemains constant
CBecomes zero at the top
DIncreases
Show answer
Answer: B (Remains constant). No horizontal force acts, so vx = v cos θ is constant.
Q3
The range of a projectile is maximum when the launch angle is:
A60°
B90°
C30°
D45°
Show answer
Answer: D (45°). R = v² sin 2θ / g is maximum when sin 2θ = 1, i.e. θ = 45°.
Q4
Two projectiles launched with the same speed at 30° and 60° will have:
ASame everything
BSame time of flight
CSame range
DSame height
Show answer
Answer: C (Same range). Complementary angles give equal ranges.
Q5
At the highest point of its path, a projectile has:
AOnly vertical velocity
BZero velocity
COnly horizontal velocity
DZero acceleration
Show answer
Answer: C (Only horizontal velocity). Vertical velocity is zero; v cos θ remains; acceleration is still g.
Q6
A ball is thrown at 20 m/s at 30° with horizontal. Its time of flight is (g = 10 m/s²):
A4 s
B3.46 s
C2 s
D1 s
Show answer
Answer: C (2 s). T = 2v sin θ / g = 2 × 20 × 0.5 / 10 = 2 s.
Q7
Newton's second law states that force equals:
AChange of velocity
BRate of change of momentum
CMass × velocity
DImpulse × time
Show answer
Answer: B (Rate of change of momentum). F = Δp/Δt.
Q8
The law of conservation of momentum is a consequence of Newton's:
AFirst law
BThird law
CLaw of gravitation
DSecond law
Show answer
Answer: B (Third law). Equal and opposite internal forces cancel, so total momentum is constant.
Q9
In an elastic collision between two equal masses with one at rest, after collision:
ABoth move with v/2
BBoth stop
CThey exchange velocities
DThey stick together
Show answer
Answer: C (They exchange velocities). The moving body stops and the other moves with its velocity.
Q10
In an inelastic collision:
AOnly momentum is conserved
BOnly KE is conserved
CBoth KE and momentum are conserved
DNeither is conserved
Show answer
Answer: A (Only momentum is conserved). Momentum is always conserved; some KE is converted to other forms.
Q11
A 2 kg gun fires a 20 g bullet at 100 m/s. The recoil speed of the gun is:
A1 m/s
B0.1 m/s
C2 m/s
D10 m/s
Show answer
Answer: A (1 m/s). 0 = 2v + 0.02 × 100 → v = −1 m/s (1 m/s backward).
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