Motion in a Plane

6 NEET-UG practice questions on Motion in a Plane, part of Physics. The first 6 are below; the first 5 with answers and explanations (tap Show answer after you have chosen), the rest in Learn with a free account.

1. Question 1 · Medium

   A river 1 km wide flows at 3 km/h. A swimmer who moves at 5 km/h in still water heads so as to reach the point directly opposite. How long does the crossing take?

   1. A12 min
   2. B7.5 min
   3. C15 min
   4. D20 min

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   Answer: C · 15 min

   To go straight across, the upstream component of the swimmer's velocity must cancel the flow, so the cross-river speed = √(5² − 3²) = 4 km/h. Time = 1/4 h = 15 min.

   • A: This is the shortest-time crossing, heading straight across at 5 km/h.
   • B: This adds the two speeds as if they were along one line.
   • D: This uses the river speed as the crossing speed.

   Remember this

   For the shortest path, resultant speed = √(v² − u²); for the shortest time, head straight across at speed v.

2. Question 2 · Easy

   A particle is in uniform circular motion. Which pair of quantities stays constant throughout the motion?

   1. AIts speed and its kinetic energy
   2. BIts velocity and its linear momentum
   3. CIts velocity and its acceleration
   4. DIts speed and its acceleration

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   Answer: A · Its speed and its kinetic energy

   In uniform circular motion only the magnitude of velocity is fixed, so speed and kinetic energy stay constant. The directions of velocity, momentum and acceleration change continuously.

   • B: Velocity and momentum both change direction continuously.
   • C: Both vectors change direction all the time.
   • D: Acceleration keeps a fixed magnitude but its direction turns towards the centre.

   Remember this

   A vector is constant only if both its magnitude and direction stay fixed.

3. Question 3 · Medium

   A football kicked from level ground stays in the air for 4 s. Ignoring air resistance and taking g = 10 m/s², what maximum height does it reach?

   1. A10 m
   2. B80 m
   3. C40 m
   4. D20 m

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   Answer: D · 20 m

   The upward part takes T/2 = 2 s, so the vertical velocity component is 10 × 2 = 20 m/s. H = (20)²/(2 × 10) = 20 m. Check: the fall from the top takes 2 s, and (1/2)(10)(2)² = 20 m. The angle is not needed.

   • A: This uses gT²/16, halving the correct result.
   • B: This uses (1/2)gT² with the full flight time.
   • C: This uses gT²/4 instead of gT²/8.

   Remember this

   H = gT²/8, whatever the speed and angle of projection.

4. Question 4 · Hard

   A boat leaves point A on one bank with the heading and speeds shown, C being directly opposite A. How far downstream of C does it land? Take sin 37° = 3/5 and cos 37° = 4/5.

   

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   1. A300 m
   2. B80 m
   3. C120 m
   4. D480 m

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   Answer: C · 120 m

   Across the river the boat moves at 5 cos 37° = 4 m/s, so t = 240/4 = 60 s. Along the river its speed is 5 − 5 sin 37° = 5 − 3 = 2 m/s, so drift = 2 × 60 = 120 m. As a check, water carries it 300 m and its heading takes it back 180 m.

   • A: Includes the river's drift but ignores the boat's upstream component.
   • B: Swaps sine and cosine when resolving the boat's velocity.
   • D: Adds the heading component to the river speed, as if heading downstream.

   Remember this

   Crossing time depends only on the across component; drift uses the net component along the river.

5. Question 5 · Medium

   A ball is thrown from level ground at an acute angle above the horizontal with speed u, and lands at the same level after time T. Ignoring air resistance, which graph shows its speed against time?

   

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   1. AGraph A
   2. BGraph B
   3. CGraph D
   4. DGraph C

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   Answer: A · Graph A

   The horizontal velocity stays constant and the vertical velocity changes uniformly with time, so speed falls smoothly to the non-zero horizontal component at T/2 and rises back to u at T. Graph A shows this rounded dip.

   • B: Graph B has zero speed at the top, which fits only a throw straight up.
   • C: Graph D has speed rising on the way up, though gravity slows the ascent.
   • D: Graph C keeps speed constant, ignoring gravity's change of the vertical velocity.

   Remember this

   At the top of a projectile path only the vertical velocity is zero; the speed equals the horizontal component.

6. Question 6 · Easy

   On a grid of 1 m squares, two displacement vectors A and B start from the same point. What is the magnitude of A + B?

   

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   1. A5 m
   2. B7 m
   3. C√5 m
   4. D4 m

   Answer and explanation in LearnFree account