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**Match the Columns**

**Ques 1: Match the following two columns.**

Column I | Column II |

(p) speed must be increasing | |

(q) speed must be decreasing | |

(r) speed may be increasing | |

(s) speed may be decreasing |

**Ans: **(a) â†’ r,s (b) â†’ r,s (c) â†’ p (d) â†’ q**Sol: ****(a)**

âˆ´ v must be increasing with time.

â‡’ speed must also be increasing with time.

(c) â†’ (p).

(d) Slope is + ive and decreasing.

âˆ´ Velocity must be decreasing with time.

â‡’ speed must also be decreasing with time. (d) â†’ (q).**Ques 2: Match the following two columns.**

Column I | Column II |

(p) speed increasing | |

(q) speed decreasing | |

(r) speed constant | |

(s) Nothing can be said |

**Ans: **(a) â†’ P (b) â†’ p (c) â†’ q (d) â†’ q**Sol:**** **

Speed increasing.

âˆ´ (a) â†’ (p).

âˆ´

âˆ´

As t > 0,

or

âˆ´

At t = 0 s

**Ques 3: The velocity-time graph of a particle moving along X-axis is shown in figure. Match the entries of Column I with entries of Column II.**

Column I | Column II |

(a) For AB, particle is | (p) Moving in +ve X-direction with increasing speed |

(b) For BC, particle is | (q) Moving in +ve X-direction with decreasing speed |

(c) For CD, particle is | (r) Moving in -ve X-direction with increasing speed |

(d) For ZXE, particle is | (s) Moving in +ve X-direction with decreasing speed |

**Ans:** (a) â†’ P (b) â†’ p (c) â†’ q (d) â†’ r

Sol: (a) From A to B, v is increasing and area is + ive.

âˆ´ (a) â†’ (p).

(b) From B to C, v is increasing and area is + ive.

âˆ´ (b) â†’ (p).

(c) From C to D, v is decreasing while area is + ive.

âˆ´ (c) â†’ (q).

(d) From D to E, v is - ive and is

increasing, area is -ive.

âˆ´ (d) â†’ (r).**Ques 4: Corresponding to velocity-time graph in one dimensional motion of a particle is shown in figure, match the following two columns.**

Column I | Column II |

(a) Average velocity between zero sec and 4 s | (p) 10 SI units |

(b) Average acceleration between 1 s and 4 s | (q) 2.5 SI units |

(c) Average speed between zero | (r) 5 SI units |

(d) Rate of change of speed at 4s | (s) None |

**Ans:** (a) â†’ (r) (b) â†’ (s) (c) â†’ (r) (d) â†’ (r)**Sol:** (a) Displacement = Area

i.e., (a) â†’ (r).

= 5.83 unit

âˆ´(b) â†’ (s)

âˆ´ (c) â†’ (s)

(d) Rate of change of velocity at t = 4 s

âˆ´ Rate of change of speed at

t = 4 s would be 5.

i.e., (d) âˆ´ (r).**Ques 5: A particle is moving along x-axis. Its x-coordinate varies with time as: x = -20 + 5t ^{2} **

Column I | Column II |

(a) Particle will cross the origin at | (p) zero sec |

(b) At what time velocity and acceleration are equal | (q) 1 s |

(c) At what time particle changes its direction of motion | (r) 2 s |

(d) At what time velocity is zero | (s) None |

**Ans:** (a) â†’ (r) (b) â†’ (q) (c) â†’ (s) (d) â†’ (p)**Sol: **(a) x = - 20 + 5t^{2}

0 = - 20 + 5t^{2}

â‡’ t = 2 s

i.e., (a) â†’ (r).

(b) x = - 20 + 5t^{2}

Velocity will be numerically equal to acceleration at t = 1 s.

Thus (b) â†’ (q).

(c) At t = 0 s x = - 20 m

t = 1 s x = - 15 m

t = 2 s x = 0 m

t = 3 s x = + 25 m

Particle is always moving along + ive x-axis.

âˆ´ (c) â†’ (s).

âˆ´ (d) â†’ (p).**Ques 6: x and y-coordinates of particle movingin x - y plane are,**

x = 1 - 2t + t^{2} and y = 4 - 4t + t^{2}

For the given situation match the following two columns.

Column I | Column II |

(a) y - component of velocity when it crosses the y-axis | (p) + 2 SI unit |

(h) x - component of velocity when it crosses the x-axis | (q) - 2 SI units |

(c) Initial velocity of particle | (r) + 4 SI units |

(d) Initial acceleration of particle | (s) None |

**Ans:** (a) â†’ (q) (b) â†’ (p) (c) â†’ (s) (d) â†’ (s)**Sol: **(a) x = 1 - 2t + t^{2}

0 = 1 - 2t + t^{2} [for particle to cross y-axis]

i.e., t = 1 s

Y = 4 - 4t + t^{2}

= - 4 + (2 x 1) [at t = 1 s]

= - 2 unit

âˆ´ (a) â†’ (q).

(b) Y = 4 - 4t + t^{2}

0 = 4 - 4t + t^{2} [For particle to cross x-axis]

i.e., t = 2 s

x = 1 - 2t + t^{2}

= - 2 + (2 x 2) [at t = 2 s]

= + 2 unit

âˆ´ Initial velocity of particle

i.e., (c) â†’ (s).

and

âˆ´ Initial acceleration of particle = 2âˆš2 unit

i.e., (d) â†’ (s).

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