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NEET PHYSICSMOTION IN A STRAIGHT LINEMedium

Question

A lift is going up. The total mass of the lift and the passenger is 1500 kg. The variation in the speed of the lift is as given in the graph. The height to which the lift takes the passenger is

A

3.6 meters

B

8 meters

C

1.8 meters

D

36 meters

Step-by-Step Solution

To find the height to which the lift takes the passenger, we need to calculate the displacement. The displacement is given by the area under the speed-time (v-t) graph .

Based on the standard graph associated with this specific problem (often found in competitive exams like NEET/AIPMT 2013), the motion corresponds to a trapezium with the following phases:

  1. Acceleration: From t=0t = 0 to t=2t = 2 s, speed increases from 0 to 3.6 m/s.
  2. Constant Speed: From t=2t = 2 to t=10t = 10 s, speed remains constant at 3.6 m/s.
  3. Deceleration: From t=10t = 10 to t=12t = 12 s, speed decreases from 3.6 m/s to 0.

Calculation: Height=Area under the curve=Area of Trapezium\text{Height} = \text{Area under the curve} = \text{Area of Trapezium} Area=12×(Sum of parallel sides)×(Height)\text{Area} = \frac{1}{2} \times (\text{Sum of parallel sides}) \times (\text{Height}) Sum of parallel sides = Total time + Time of constant motion = 12 s+(10−2) s=12+8=20 s12 \text{ s} + (10 - 2) \text{ s} = 12 + 8 = 20 \text{ s}. Height of graph = Maximum speed = 3.6 m/s3.6 \text{ m/s}.

Height=12×(20)×3.6\text{Height} = \frac{1}{2} \times (20) \times 3.6 Height=10×3.6=36 meters\text{Height} = 10 \times 3.6 = 36 \text{ meters}

The mass of the lift (1500 kg) is not required for calculating the displacement from the v-t graph.

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from MOTION IN A STRAIGHT LINE. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSMOTION IN A STRAIGHT LINEpassengervariationheightpassenger

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