Kinematics-1D
182 Questions
Start Errorless Test
Q176
Errorless
7. Graphical Questions
MCQ
An object is dropped from rest. Its $v - t$ graph is
A.
B.
C.
D.
E.
Q177
Errorless
7. Graphical Questions
MCQ
The motion of an v(m/sec) airplane is represented by velocity-time graph as shown below. The distance covered by airplane in the first 30.5 second is ____ km
A.
9
B.
6
C.
3
D.
12
Q178
Errorless
8. JEE Section
MSQ
A particle moves with an initial velocity $v_{0}$ and retardation $\alpha v$ , where $v$ is its velocity at any time $t$
A.
The particle will cover a total distance $v_{0} / \alpha$
B.
The particle will come to rest after a time $1/\alpha$
C.
The particle will continue to move for a very long time
D.
The velocity of the particle will become $v_{0}/2$ after a time $1/\alpha$
Q179
Errorless
8. JEE Section
MCQ
Average velocity during the first 20 seconds
A.
$-10\mathrm{m / s}$
B.
$10~m / s$
C.
Zero
D.
None of these
Q180
Errorless
8. JEE Section
MCQ
Find the average acceleration during the first 20 seconds
A.
$\sqrt{3} m / s^2$
B.
$-\sqrt{3} m / s^2$
C.
Zero
D.
$1m / s^2$
Q181
Errorless
8. JEE Section
MCQ
During which interval is the motion retarded
A.
0 - 10
B.
10 - 20
C.
5 - 15
D.
None of these
Q182
Errorless
9. Matrix Match Type Questions
Numerical
A particle moves along a straight line such that its displacement s varies with time t as $s = \alpha + \beta t + \gamma t ^ {2}$
Match the following Column I with Column-II:
Match the following Column I with Column-II:
| Column-I | Column-II | ||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
|
Correct Answer: A → q; B → p; C → s; D → r
Explanation:
$\mathbf{A} \rightarrow \mathbf{q}; \mathbf{B} \rightarrow \mathbf{p}; \mathbf{C} \rightarrow \mathbf{s}; \mathbf{D} \rightarrow \mathbf{r}$ $s = \alpha + \beta t + \gamma t^2$ Velocity $v = \frac{ds}{dt} = \beta + 2\gamma t$ ;
Acceleration $a = \frac{d^2 s}{dt^2} = 2\gamma$ Thus particle moves with constant acceleration $2\gamma$ . $\therefore (A) \rightarrow q$ At $t = 1s, v = \beta + 2\gamma \therefore (C) \rightarrow s$ At $t = 0, s = \alpha$ $\therefore (D) \rightarrow r$ Average velocity during third second, $v_{av} = \frac{(\beta + 2\gamma t)_{t=2s} + (\beta + 2\gamma t)_{t=3s}}{2}$ $= \frac{\beta + 4\gamma + \beta + 6\gamma}{2} = \beta + 5\gamma \quad \therefore (B) \rightarrow p.$
Acceleration $a = \frac{d^2 s}{dt^2} = 2\gamma$ Thus particle moves with constant acceleration $2\gamma$ . $\therefore (A) \rightarrow q$ At $t = 1s, v = \beta + 2\gamma \therefore (C) \rightarrow s$ At $t = 0, s = \alpha$ $\therefore (D) \rightarrow r$ Average velocity during third second, $v_{av} = \frac{(\beta + 2\gamma t)_{t=2s} + (\beta + 2\gamma t)_{t=3s}}{2}$ $= \frac{\beta + 4\gamma + \beta + 6\gamma}{2} = \beta + 5\gamma \quad \therefore (B) \rightarrow p.$