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Motion in A Straight Line question

2004 · Shift 0 · Q188
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Motion in A Straight Line question

2004 · Shift 0 · Q188

JEE MainPhysicsMotion in A Straight LineMCQ+4 / −1
An automobile travelling with speed of 60 km/h, can brake to stop within a distance of 20 m. If the car is going twice as fast, i.e 120 km/h, the stopping distance will be
  1. A
    60 m
  2. B
    40 m
  3. C
    20 m
  4. D
    80 m
View written solutionFree

Correct answer: D

  1. Use the kinematic relation for braking

When a car brakes with the same braking force, the deceleration aaa is constant. We use:

v2=u2+2asv^2 = u^2 + 2asv2=u2+2as

For stopping, final speed v=0v=0v=0, so:

0=u2+2as0 = u^2 + 2as0=u2+2as

s=−u22as = -\frac{u^2}{2a}s=−2au2​

Since aaa is the same in both cases, the stopping distance is proportional to the square of the initial speed:

s∝u2s \propto u^2s∝u2

  1. Compare the two cases

Initial case:

  • speed u1=60 km/hu_1 = 60\ \text{km/h}u1​=60 km/h
  • stopping distance s1=20 ms_1 = 20\ \text{m}s1​=20 m

Second case:

  • speed u2=120 km/h=2u1u_2 = 120\ \text{km/h} = 2u_1u2​=120 km/h=2u1​

So,

s2s1=(u2u1)2=22=4\frac{s_2}{s_1} = \left(\frac{u_2}{u_1}\right)^2 = 2^2 = 4s1​s2​​=(u1​u2​​)2=22=4

Thus,

s2=4s1=4×20=80 ms_2 = 4s_1 = 4 \times 20 = 80\ \text{m}s2​=4s1​=4×20=80 m

  1. Check options
  • A: 60 m60\ \text{m}60 m ❌
  • B: 40 m40\ \text{m}40 m ❌
  • C: 20 m20\ \text{m}20 m ❌
  • D: 80 m80\ \text{m}80 m ✅

Therefore, the correct answer is D.

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