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) → r,s (b) → r,s (c) → p (d) → q
Sol:
(a)
∴ v must be increasing with time.
⇒ speed must also be increasing with time.
(c) → (p).
(d) Slope is + ive and decreasing.
∴ Velocity must be decreasing with time.
⇒ speed must also be decreasing with time. (d) → (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) → P (b) → p (c) → q (d) → q
Sol:
Speed increasing.
∴ (a) → (p).
∴
∴
As t > 0,
or
∴
At t = 0 s
Ques 3: The velocitytime graph of a particle moving along Xaxis 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 Xdirection with increasing speed 
(b) For BC, particle is  (q) Moving in +ve Xdirection with decreasing speed 
(c) For CD, particle is  (r) Moving in ve Xdirection with increasing speed 
(d) For ZXE, particle is  (s) Moving in +ve Xdirection with decreasing speed 
Ans: (a) → P (b) → p (c) → q (d) → r
Sol: (a) From A to B, v is increasing and area is + ive.
∴ (a) → (p).
(b) From B to C, v is increasing and area is + ive.
∴ (b) → (p).
(c) From C to D, v is decreasing while area is + ive.
∴ (c) → (q).
(d) From D to E, v is  ive and is
increasing, area is ive.
∴ (d) → (r).
Ques 4: Corresponding to velocitytime 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) → (r) (b) → (s) (c) → (r) (d) → (r)
Sol: (a) Displacement = Area
i.e., (a) → (r).
= 5.83 unit
∴(b) → (s)
∴ (c) → (s)
(d) Rate of change of velocity at t = 4 s
∴ Rate of change of speed at
t = 4 s would be 5.
i.e., (d) ∴ (r).
Ques 5: A particle is moving along xaxis. Its xcoordinate varies with time as: x = 20 + 5t^{2}
For the given equation match the following two columns
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) → (r) (b) → (q) (c) → (s) (d) → (p)
Sol: (a) x =  20 + 5t^{2}
0 =  20 + 5t^{2}
⇒ t = 2 s
i.e., (a) → (r).
(b) x =  20 + 5t^{2}
Velocity will be numerically equal to acceleration at t = 1 s.
Thus (b) → (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 xaxis.
∴ (c) → (s).
∴ (d) → (p).
Ques 6: x and ycoordinates 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 yaxis  (p) + 2 SI unit 
(h) x  component of velocity when it crosses the xaxis  (q)  2 SI units 
(c) Initial velocity of particle  (r) + 4 SI units 
(d) Initial acceleration of particle  (s) None 
Ans: (a) → (q) (b) → (p) (c) → (s) (d) → (s)
Sol: (a) x = 1  2t + t^{2}
0 = 1  2t + t^{2} [for particle to cross yaxis]
i.e., t = 1 s
Y = 4  4t + t^{2}
=  4 + (2 x 1) [at t = 1 s]
=  2 unit
∴ (a) → (q).
(b) Y = 4  4t + t^{2}
0 = 4  4t + t^{2} [For particle to cross xaxis]
i.e., t = 2 s
x = 1  2t + t^{2}
=  2 + (2 x 2) [at t = 2 s]
= + 2 unit
∴ Initial velocity of particle
i.e., (c) → (s).
and
∴ Initial acceleration of particle = 2√2 unit
i.e., (d) → (s).
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