Class 12 Maths Mcqs

Q:

The distance s of a particle moving along a straight line from a fixed-pointO on the line at time t seconds after start is given by x = (t – 1)²(t – 2)². What will be the distance of the particle from O when its velocity is zero?

A) 4/27 units B) 4/23 units
C) 4/25 units D) 4/35 units
 
Answer & Explanation Answer: A) 4/27 units

Explanation: Let v be the velocity of the particle at time t seconds after start (that is at a distance s from O). Then,
v = ds/dt = d[(t – 1)²(t – 2)²]/dt
Or v = (t – 2)(3t – 4)
Clearly, v = 0, when (t – 2)(3t – 4) = 0
That is, when t = 2
Or 3t – 4 = 0 i.e., t = 4/3
Now, s = (t – 1)(t – 2)²
Therefore, when t = 4/3, then s = (4/3 – 1)(4/3 – 2)² = 4/27
And when t = 2, then s =(2 – 1)(2 – 2)² = 0
Therefore, the velocity of the particle is zero, when its distance from O is 4/27 units and when it is at O.

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Q:

The distance x of a particle moving along a straight line from a fixed point on the line at time t after start is given by t = ax² + bx + c (a, b, c are positive constants). If v be the velocity of the particle and u(≠0) be the initial velocity of the particle then which one is correct?

A) 1/v² + 1/u² = 4at B) 1/v² + 1/u² = -4at
C) 1/v² – 1/u² = 4at D) 1/v² – 1/u² = -4at
 
Answer & Explanation Answer: C) 1/v² – 1/u² = 4at

Explanation: Not available for this question

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Q:

A particle moves in a horizontal straight line under retardation kv³, where v is the velocity at time t and k is a positive constant. If initial velocity be u and x be the displacement at time,then which one is correct?

A) 1/v² = 1/2u² + 2kt B) 1/v² = 1/2u² – 2kt
C) 1/v² = 1/u² – 2kt D) 1/v² = 1/u² + 2kt
 
Answer & Explanation Answer: D) 1/v² = 1/u² + 2kt

Explanation: Not available for this question

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17
Q:

A particle moves with uniform acceleration along a straight line and describes distances 21m, 43m and 91m at times 2, 4 and 7 seconds, respectively.What is the velocity of the particle in 3 seconds?

A) 11m/sec B) 31 cm/sec
C) 21m/sec D) 41m/sec
 
Answer & Explanation Answer: A) 11m/sec

Explanation: Not available for this question

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Q:

A particle moves with uniform acceleration along a straight line and describes distances 21m, 43m and 91m at times 2, 4 and 7 seconds,respectively.What is the distance described by the particle in 3 seconds?

A) 30 cm B) 31 cm
C) 32 cm D) 33 cm
 
Answer & Explanation Answer: B) 31 cm

Explanation: Not available for this question

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16
Q:

A particle moving in a straight line traverses a distance x in time t. If t = x²/2 + x, then which one is correct?

A) The retardation of the particle is the cube of its velocity B) The acceleration of the particle is the cube of its velocity
C) The retardation of the particle is the square of its velocity D) The acceleration of the particle is the square of its velocity
 
Answer & Explanation Answer: A) The retardation of the particle is the cube of its velocity

Explanation: Not available for this question

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15
Q:

A particle moves in a straight line and its velocity v at time t seconds is given byv = 3t² – 4t + 5 cm/second. What will be the distance travelled by the particle during first 3 seconds after the start?

A) 21 cm B) 22 cm
C) 23 cm D) 24 cm
 
Answer & Explanation Answer: D) 24 cm

Explanation: Not available for this question

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Q:

A particle moves in a straight-line OA; the distance of the particle from O at time t seconds is x ft, where x = a + bt + ct² (a, b > 0). What will be the nature of motion of the particle when c = 0?

A) Uniform retardation B) Uniform speed
C) Uniform acceleration D) Uniform velocity
 
Answer & Explanation Answer: D) Uniform velocity

Explanation: We have, x = a + bt + ct²  ……….(1)
Let, v and f be the velocity and acceleration of a particle at time t seconds.
Then, v = dx/dt = d(a + bt + ct²)/dt = b + ct   ……….(2)
And f = dv/dt = d(b + ct)/dt = c  ……….(3)
Clearly, when c = 0, then f = 0 that is, acceleration of the particle is zero.
Hence in this case the particle moves with an uniform velocity.

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