Motion — Set 1

Correct Answer: A. m/s^2

• **m/s²** = Acceleration is defined as the rate of change of velocity per unit time; velocity is m/s, dividing by seconds gives m/s². • **[L T⁻²]** — the dimensional formula confirms no mass dimension; it equals length divided by time squared. • 💡 Wrong-option analysis: m/s: this is the unit of velocity, one level before dividing by time; N: Newton is the unit of force (kg·m/s²) which includes mass; m²/s: this is a non-standard combination that does not represent any common physical quantity.

Correct Answer: C. 25 m

• **25 m** = Using s = ut + ½at² with u = 0, a = 2 m/s², t = 5 s: s = 0 + ½×2×25 = 25 m. • **s = ½at² = ½×2×25 = 25 m** — starting from rest (u = 0) simplifies the second equation of motion. • 💡 Wrong-option analysis: 50 m: error of using s = at² (missing the ½ factor); 15 m: incorrect arithmetic with the formula; 10 m: error of substituting t = 5 directly as distance without using the equation.

Correct Answer: A. Distance is a scalar, displacement is a vector

• **Distance is a scalar, displacement is a vector** = Distance measures total path length (magnitude only), while displacement is the straight-line change in position and requires a direction. • **scalar vs vector** — distance is always non-negative; displacement can be zero even when distance is non-zero (e.g., a round trip). • 💡 Wrong-option analysis: Displacement is always greater than distance: false — displacement ≤ distance; they are equal only for straight-line one-way motion; Distance can be negative, displacement cannot: reversed — distance is always positive; displacement can be negative; Both are always equal: false — only when the path is a single straight line without reversal.

Correct Answer: A. Acceleration

• **Acceleration** = The slope of a velocity–time graph equals Δv/Δt, which is the definition of acceleration. • **slope = Δv/Δt** — a steeper v–t line means greater acceleration; a horizontal line means constant velocity (zero acceleration). • 💡 Wrong-option analysis: Displacement: displacement is the area under the v–t graph, not the slope; Momentum: momentum = mv cannot be read as a slope of a v–t graph; Speed: speed is the y-axis value, not the slope.

Correct Answer: A. 4 km/h

• **4 km/h** = Total distance = 6 km; time going = 3/3 = 1 h, time returning = 3/6 = 0.5 h; total time = 1.5 h; avg speed = 6/1.5 = 4 km/h. • **formula: 2v₁v₂/(v₁+v₂) = 2×3×6/(3+6) = 4 km/h** — for equal distances the harmonic mean of speeds gives the correct average. • 💡 Wrong-option analysis: 3 km/h: this is just the speed on the first leg, not the average; 5 km/h: not obtainable from correct formula; 4.5 km/h: this is the arithmetic mean (3+6)/2, which is wrong for equal distances.

Correct Answer: D. Tangent to the circle

• **Tangent to the circle** = In uniform circular motion the instantaneous velocity is always directed along the tangent to the circular path, perpendicular to the radius. • **v ⊥ r** — this is why objects fly off tangentially when released from circular motion (e.g., a stone released from a sling). • 💡 Wrong-option analysis: Radius towards the center: this is the direction of centripetal acceleration, not velocity; Radius away from the center: this is the direction of the centrifugal pseudo-force, not velocity; Vertical direction only: velocity direction depends on position on the circle, it is always tangential.

Correct Answer: D. -5 m/s^2

• **-5 m/s²** = Using a = (v−u)/t with v = 0, u = 20 m/s, t = 4 s: a = (0−20)/4 = −5 m/s². • **a = Δv/Δt = −20/4 = −5 m/s²** — the negative sign indicates deceleration (opposing the direction of motion). • 💡 Wrong-option analysis: −8 m/s²: would require stopping in 2.5 s, not 4 s; −2 m/s²: would require 10 s to stop; −4 m/s²: would require 5 s to stop.

Correct Answer: D. 1 m/s = 3.6 km/h

• **1 m/s = 3.6 km/h** = Since 1 km = 1000 m and 1 h = 3600 s: 1 m/s = (1/1000 km)/(1/3600 h) = 3600/1000 = 3.6 km/h. • **multiply by 3.6** — to convert m/s to km/h, multiply by 3.6; to convert km/h to m/s, divide by 3.6. • 💡 Wrong-option analysis: 1.6 km/h: not a standard conversion factor for m/s to km/h; 36 km/h: ten times too large — error of multiplying by 36 instead of 3.6; 0.36 km/h: ten times too small — error of dividing by 3.6 instead of multiplying.

Correct Answer: B. 9.8 m/s^2 downward

• **9.8 m/s² downward** = Near Earth's surface, gravity accelerates falling objects at approximately 9.8 m/s² directed downward (toward Earth's center). • **g ≈ 9.8 m/s²** — this value is independent of the mass of the falling object; in problems it is often approximated as 10 m/s². • 💡 Wrong-option analysis: Depends on mass only: false — Galileo showed all masses fall at the same rate in a vacuum; 9.8 m/s² upward: wrong direction — gravity is always attractive and pulls downward; 0 m/s²: zero acceleration would mean no gravity, which is not the case near Earth's surface.

Correct Answer: B. 11 m/s

• **11 m/s** = Using v = u + at with u = 5 m/s, a = 2 m/s², t = 3 s: v = 5 + 6 = 11 m/s. • **v = u + at = 5 + 2×3 = 11 m/s** — this is the first equation of motion for constant acceleration. • 💡 Wrong-option analysis: 5 m/s: this is just the initial velocity, ignoring the acceleration; 6 m/s: this is only the change in velocity (at = 6) without adding the initial velocity; 9 m/s: arithmetic error, possibly using t = 2 instead of t = 3.