Speed

Q. The period of oscillation of a simple pendulum is given by $T=2\pi \sqrt{\frac{l}{g}}$, where $l$ is about $100\text{cm}$ and is known to have $1\text{mm}$ accuracy. The period is about $2\text{s}$. The time of $\text{100}$ oscillations is measured by a stop watch of least count $0.1\text{s}$. The percentage error in $g$ is

1. $0.01\text{\%}$
2. $1\text{\%}$
3. $0.2\text{\%}$
4. $0.1\text{\%}$

Q.

What does the slope of a distance-time graph indicate?

Q. A man can swim with a speed of $4.0{\text{kmh}}^{-1}$ in still water. How long does he take to cross a river $1.0\text{km}$ wide if the river flows steadily at $3.0{\text{kmh}}^{-1}$ and he makes his strokes normal to the river current? How far down the river does he go when he reaches the other bank?

Q. The distance of a galaxy is of the order of ${10}^{25}m$ . Calculate the order of magnitude of time taken by light to reach us from the galaxy.

Q.

A body covers half of its journey with a speed of $60{\mathrm{ms}}^{-1}$ and the other half with a speed of $40{\mathrm{ms}}^{-1}$. Then find the average speed during the whole journey.

Q. A man is crossing a river flowing with velocity of $5m/s$. He reaches a point directly across at a distance of $60m$ in $5sec$⁡. His velocity in still water should be

1. $10m/s$
2. $13m/s$
3. $5m/s$
4. $12m/s$

Q. A grindstone starts from rest and has a constant-angular acceleration of $4.0rad/se{c}^2$. The angular displacement and angular velocity, after $4sec$ will respectively be

1. $32rad,64rad/sec$
2. $32rad,16rad/sec$
   
3. $16rad,32rad/sec$
4. $64rad,32rad/sec$

Q. The length of a pendulum is measured as 20.0 cm. The time interval for 100 oscillations is measured as 90 s with a stop watch of 1 s resolution. Find the approximate percentage error in g to the nearest integer.

Q. A monkey climbs up a slippery pole for 3 second and subsequenty slips for 3 second.its velocity at time t is given by

$v\left(t\right)=2t(3-t)$; $0<t<3s$ and

$v\left(t\right)=-(t-3)(6-t)$; $3<t<6s$
in $m/s$. it repeats this cycle till it reaches the height of $20m$. At what time is its average velocity maximun?

Q. A car is going in south with a speed of $5m/s$. To a man sitting in car a bus appears to move towards west with a speed of $2\sqrt{6})m/s$. What is the actual speed of the bus?

1. $3m/s$
2. $4m/s$
3. None of these
4. $7m/s$

Q. A stone is thrown upwards with a velocity $50m/s$. Another stone is simultaneously thrown downwards from the same location with a velocity $50m/s$. When the first stone is at the highest point, the velocity of the second stone is (Take $g=10m/s^2$):

1. $100m/s$
2. zero
3. $150m/s$
4. $50m/s$

Q. An artificial satellite is revolving in a circular orbit at height of $1200\text{km}$ above the surface of planet. If the radius of the planet is $6400\text{km}$ and mass is $9\times {10}^{23}\text{kg}$, the orbital speed is ($G=6.7\times {10}^{-11}$${\text{Nm}}^2/{\text{kg}}^2$)

1. $2.1{\text{kms}}^{-1}$
2. $2.8{\text{kms}}^{-1}$
3. $9{\text{kms}}^{-1}$
4. $1{\text{kms}}^{-1}$

Q. The end $A$ of a rod of length $l$ when it moves with a velocity ${\overrightarrow{v}}_A=v\hat{i}$ . If the rod rotates with an angular velocity $\overrightarrow{\omega }=-\frac{v}{2l}\hat{k}$ the instantaneous axis of rotation is located

1. at a distance $l$ from $A$
2. at a distance $1.5l$ from $A$
3. at a distance $2.5l$ from $A$
4. at a distance $2l$ from$A$

Q. The tip of the seconds hand of a clock takes $60$ seconds to move once on the circular dial of the clock. If the radius of the dial of the clock be $10.5\text{cm}$ then calculate the speed of the tip of the seconds hand.

1. $1.1\text{m/s}$
2. $2.2\text{m/s}$
3. $0.011\text{m/s}$
4. $0.11\text{m/s}$

Q. Two towns $A\text{and}B$ are connected by a regular bus service with a bus leaving in either direction every $T\text{minutes}$. A man cycling with a speed of $20km/hr$ in the direction $A\text{to}B$ notices that a bus goes past him every $18min$ ⁡in the direction of his motion, and every $6min$ ⁡in the opposite direction. What is the period $T$ of the bus service, and at what speed (assumed constant) do the buses ply on the road?

Q. It takes one minute for a passenger standing on an escalator to reach the top. If the escalator does not move it takes him $3$ minutes to walk up. How long will it take for the passenger to arrive at the top if he walks up the moving escalator?

1. $25sec$
2. $30sec$
3. $35sec$
4. $45sec$

Q. A boy standing at a corner noticed a thief on bike moving with $54km/h$. After some time, a police jeep crosses him with speed $72km/h$. If the jeep catches the thief at a distance of $1km$ from the boy, then the time gap (in $s$) between the bike and the jeep, when they cross the boy, is

Q.

The _______ of a distance versus time graph is speed.

Q. "The tip of second hand" of the clock takes $60\text{s}$ to move once on the circular dial of the clock. If the length of the second hand is $10\text{cm}$, calculate the speed of the tip of the second hand clock ?

$(\pi =22/7)$

1. $0.04\text{m/s}$
2. $0.02\text{m/s}$
3. $0.01\text{m/s}$
4. $0.03\text{m/s}$

Q.

A car travels $40km$ at an average speed of $80km{h}^{-1}$ and then travels $40km$ at an average speed of $40km{h}^{-1}$ . The average speed of the car for this $80km$ trip is

1. $40km{h}^{-1}$

2. $45km{h}^{-1}$

3. $53km{h}^{-1}$

4. $56km{h}^{-1}$

Q. A passenger train of length $90\text{m}$ travels at a speed of $120\text{km/h}$. Another freight train of length $180\text{m}$ travels at a speed of $60\text{km/h}$. What is the ratio of the time taken by the passenger train to cross the freight train when they are moving in the same direction and when they are moving in opposite directions?

1. 1 : 1
2. 1 : 3
3. 3 : 1
4. 3 : 2

Q. Suppose a car's standard tires are replaced with tires
$1.50$ times larger in diameter. What will the car's speedometer reading be?

1. $2.25$ times too high
2. $2.25$ times too low
3. $1.50$ times too low
4. $1.50$ times too high

Q. A truck travelling due north at $20m/s$ turns west and travels at the same speed. The change in its velocity be

1. $40m/sS-W$
2. $20\sqrt{2}m/sS-W$
3. $40m/sN-W$
4. $20\sqrt{2}m/sN-W$

Q. In an experiment of simple pendulum; time period measured was 50s for 25 vibrations. When the length of the simple pendulum was taken 100 cm. If the least count of Stop watch is 0.1 s and that of metre scale is 0.1cm, Calculate the maximum possible percentage error in the measurement of value of g.

Q. The velocity-time graph of a particle in one-dimensional motion is shown in Fig:
Which of the following formulae are correct for describing the motion of the particle over the time-interval $t_1\text{to}{t}_2$:

$A$: $x\left(t_2\right)=x\left(t_1\right)+v\left(t_1\right)(t_2-t_1)+\left(1/2\right)a(t_2-t_1{)}^2$

$B$: $v\left(t_2\right)=v\left(t_1\right)+a(t_2-t_1)$

$C$: $v_{\text{average}}=\left(x\right(t_2)-x(t_1\left)\right)/(t_2-t_1)$

$D$: $v_{\text{average}}=\left(v\right(t_2)-v(t_1\left)/\right(t_2-t_1\left)\right)$

$E$: $x\left(t_2\right)=x\left(t_1\right)+v_{\text{average}}(t_2-t_1)+\left(1/2\right)a_{\text{average}}(t_2-t_1{)}^2$

$F$: $x\left(t_2\right)-x\left(t_1\right)=$area under the $v-t$ curve bounded by the $t-\text{axis}$ and the dotted line shown .

Q. Shown in the figure is a rod which moves with $v=2m/\sec$ and rotates with $\omega =2\pi rad/\sec$. The instantaneous axis of rotation is

1. $\frac{3}{\pi }m$ from center of rod
2. $\frac{1}{\pi }m$ from center of rod
3. $\frac{2}{3\pi }m$ from center of rod
4. $\frac{3}{2\pi }m$ from center of rod

Q. A car covers $\frac{1}{3}$ part of total distance with a speed of $20km/hr$ and second $\frac{1}{3}$ part with a speed of $30km/hr$ and the last $\frac{1}{3}$ part with a speed of $60km/hr$. The average speed of the car is

1. $55km/hr$
   
2. $45km/hr$
   
3. $30km/hr$
   
4. $37.3km/hr$
   

Q. A particle moving in a straight line covers first half of the distance into two equal time intervals with speed of 2 m/s and 4 m/s respectively, and second half with speed of 5m/s. The average speed of the particle is

Q.

A displacement

1. Is always positive.

2. Is always negative.

3. May be positive as well as negative.

4. Is neither positive nor negative.

Q. the least count of a stopwatch is 0.2 second the time of 20 oscillation of a pendulum is measured to be 25 second the percentage error in time period is