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Motion in a Straight Line · Question 41

AIPMT 2005MCQMedium📈 Topic in 25% papers+4−1
1

The displacement x of a particle varies with time t as x = ae- t + be t, where a, b, and are positive constants. The velocity of the particle will

  1. be independent of
  2. drop to zero when =
  3. go on decreasing with time
  4. go on increasing with time.

Answer

(4) go on increasing with time.

Solution

v = dxdt = -a e- t + b e t

dvdt = a 2 e- t + b 2 e t

a, b, , are positive, both terms are positive dvdt > 0 at all times

The velocity goes on increasing with time.

Answer: (4)

AIPMT 2005

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2

A man throws balls with the same speed vertically upwards one after the other at an interval of 2 seconds. What should be the speed of the throw so that more than two balls are in the sky at any time ? (Given g = 9.8 m/s2)

  1. more than 19.6 m/s
  2. at least 9.8 m/s
  3. any speed less than 19.6 m/s
  4. only with speed 19.6 m/s.
AIPMT 2003
3

If a ball is thrown vertically upwards with speed u, the distance covered during the last t seconds of its ascent is

  1. ut
  2. 12gt2
  3. ut - 12gt2
  4. (u + gt)t.
AIPMT 2003
4

A particle is thrown vertically upward. Its velocity at half of the height is 10 m/s, then the maximum height attained by it is (g = 10 m/s2)

  1. 8 m
  2. 20 m
  3. 10 m
  4. 16 m
AIPMT 2001
5

Motion of a particle is given by equation s = (3t3 + 7t2 + 14t + 8) m. The value of acceleration of the particle at t = 1 s is

  1. 10 m/s2
  2. 32 m/s2
  3. 23 m/s2
  4. 16 m/s2
AIPMT 2000

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