Paper Questions (Raw)
Q1. The displacement and the distance covered by a body are same, when
1) only magnitude of velocity remains constant.
2) only the direction of velocity remains constant.
3) both (1) and (2).
4) None of the above.
Q2. The initial and final positions, respectively of an object along (x)-axis are (5 m) and (-2 m). The distance travelled and displacement of object is
1) (7 m, 7 m)
2) (5 m, 2 m)
3) (7 m,-7 m)
4) (7 m,-3 m)
Hint: Distance travelled (=5+2=7m) Displacement (= - 2 - 5 = - 7 m)
Q3. A motor car covers half part of total distance with speed (10 km / hr), half of the second part with speed (20 km / hr) and the rest with speed (60 km / hr). What is the average speed of the car?
1) (45 km / hr)
2) (22.5 km / hr)
3) (18 km / hr)
4) (15 km / hr)
Hint: Total distance covered
(= s)(s/2 = 10 t_0 => t_0 = s/20)(s/4 = 20 t_1 => t_1 = s/80)(s/4 = 60 t_2 => t_2 = s/240)∴ Total time,
(t = t_0 + t_1 + t_2 = s/20 + s/80 + s/240 = 16 s/240)$$ \therefore \bar{v}=\frac{s}{t}=\frac{s}{16 s / 240}=\frac{240}{16}=15 km / hr $$
Q4. One car moving on a straight road covers one third of the distance with (20 km / hr) and the rest with (60 km / hr). The average speed is
1) (40 km / hr)
2) (80 km / hr)
3) (46 \frac{2}{3} km / hr)
4) (36 km / hr)
Hint: (Average speed = \frac{Total distance}{Total time} = \frac{x}{t_1+t_2} = \frac{x}{\frac{x / 3}{v_1}+\frac{2 x / 3}{v_2}} = \frac{1}{\frac{1}{3 \times 20}+\frac{2}{3 \times 60}} = \frac{3 \times 60}{5} = 36 km / hr)
Q5. A particle moves along (x)-axis with speed (6 m / s) for the first half distance of a journey and the second half distance with a speed (3 m / s). The average speed in the total journey is
1) (5 m / s)
2) (4.5 m / s)
3) (4 m / s)
4) (2 m / s)
Hint: Total distance covered
(= s)$$ \begin{aligned} & \frac{s}{2}=6 t_1 \Rightarrow t_1=\frac{s}{12} \\ & \frac{s}{2}=3 t_2 \Rightarrow t_2=\frac{s}{6} \end{aligned} $$
∴ Total time,
(t = t_1 + t_2 = s/12 + s/6 = 3 s/12 = s/4)$$ \therefore \overline{v}=\frac{s}{t}=\frac{s}{s / 4}=4 m / s $$
Q6. If a particle travels in a straight line in same direction with a velocity of (5 m / s) for 2 seconds and (10 m / s) for 3 s , then the average velocity is
1) (8 m / s)
2) (7.5 m / s)
3) (6.6 m / s)
4) (3.3 m / s)
Hint: (\overline{v}=\frac{total dis tance}{total time} = \frac{(5 \times 2)+(10 \times 3)}{5} = \frac{40}{5} = 8 m / s)
Q7. A particle covers half of its total distance with speed (v) and the rest half distance with speed (v / 3). Its average speed during the complete journey is
1) (\frac{3 v}{8})
2) (\frac{3 v}{4})
3) (\frac{v}{2})
4) (\frac{4 v}{5})
Hint: (Average speed = \frac{Total distance}{Total time} = \frac{x}{t_1+t_2} = \frac{x}{\frac{x / 2}{v}+\frac{x / 2}{v / 3}} = \frac{x}{\frac{x}{2 v}+\frac{3 x}{2 v}} = \frac{2 v x}{4 x} = \frac{v}{2})
Q8. A bus travelled the first one-third distance at the speed of (10 km hr^{-1}), the next one-third at (20 km hr^{-1}), and the last one-third at (60 km hr^{-1}). The average speed of the bus is
1) (18 km hr^{-1})
2) (16 km hr^{-1})
3) (9 km hr^{-1})
4) (48 km hr^{-1})
Hint: Let total distance (= 3 d)Time taken for first one-third journey (= \frac{d}{10})Time for next one-third journey (= \frac{d}{20})Time for last one third journey (= \frac{d}{60})Therefore, the total time of journey is (t = \frac{d}{10} + \frac{d}{20} + \frac{d}{60} = \frac{10 d}{60} = \frac{d}{6})Average speed (= \frac{Totaldis tance}{Totaltime} = \frac{3 d}{d / 6} = 18 km / hr)