Velocity Displacement Relationship

Q.

The equation of a progressive wave is given by $y=asin(628t-31.4x)$ If the distances are expressed in cms and time in seconds, then the wave velocity will be

[DPMT 1999]

1. 314 cm/sec

2. 400 cm/sec

3. 20 cm/sec

4. 628 cm/sec

Q. 19.The position vector of a particle R vector as a function of time is given by- R vector=4sin(2pit)i+4cos(2pit)j Where R is in m, t is in sec & i & j denote unit vectors along x & y directions respectively.Which one of the following statements is wrong for the motion of particle? 1 patglh of the particle is a circle of radius 4 m 2 acceleration vectors is along -R vector 3 magnitude of acceleration vector is v2/R where v is the velocity of particle 4 magnitude of the velocity of particle is 8 m/sec

Q. 33.The x and y coordinate of the particle at any time t are given by x = 7t + 4t*2 and y = 5t , where x and y are in metre and time t in seconds. The acceleration of the particle at t = 5 sec is

Q. The acceleration of the particle moving in straight line is given by a = 4t -30where a is in m/s, and t is in s. The velocity and displacement as function of time is(the initial displacement at t = 0 s is s = -5m/s and the initial velocity is v = 3 m/s)

Q. two simple pendulumn of lenght 5m and 20 m respectively are given small linear displacement in one direction at the same time .They will again in same phase when pendulum of shhorter lenght has completed osccillatio

Q. A particle executes SHM with a period of 16 s. At time t=2s, the particle crosses the mean position while at t=4s, its velocity is 4 m/s. Amplitude of motion in metre is

Q. A particle executes linear simple harmonic motion with an amplitude of $3\text{cm}$. When the particle is at $2\text{cm}$ from the mean position, the magnitude of its velocity is equal to that of its acceleration. Find the time period in seconds.

1. $\frac{\sqrt{5}}{2\pi }$
2. $\frac{4\pi }{\sqrt{5}}$
3. $\frac{2\pi }{\sqrt{3}}$
4. $\frac{\sqrt{5}}{\pi }$

Q.

The second hand of a clock is 2.0 cm long .calculate the speed of the tip of the hand, the velocity at 0 seconds and at 15 seconds, the change in velocity from 0.0 to 15 seconds, and average acceleration.

Q.

For a simple pendulum, the graph between g and $T^2$ will be

1. Circle

2. Square

3. Hyperbola

4. Straight line

Q. Position x of a moving particle with time t is given by x= 6(t-e^{-2t}). Initial and final velocity of the particle will be respectively (1) 6m/s and 12m/s (2) 6m/s and 18m/s (3) 18m/s and 12m/s (4) 18m/s and 6m/s

Q.

A car travelling at 36km/h^-1 due North turns West in 5 seconds and maintains the same speed. What is the acceleration of the car?

1. 4ms^-2South West

2. 2√2 ms^-2South West

3. 2ms^-2South West

4. √2ms^-2South West

Q. 4. A car moving along a straight road at a speed ofu m/s applies brakes at t = 0 second. The ratioTrof distances travelled by the car during 3rd and8th second is 15:: 13. The car covers a distanceof 0.25 m in the last second of its travel. Thereforethe acceleration a(in m/s2) and the speed u(in m/s) of the car are respectively \lbrack NSEP 2016\rbrack(1) -0.1, 16(2) -0.2, 12(3) -0.5, 20(4) -0.1, 16

Q. A car travels first 10 seconds with uniform acceleration of 2 m/s^2 from rest on straight road and then travels with zero acceleration for next 10 seconds.The average speed of entire journey is

Q. A block with a mass of $1\text{kg}$ is connected to a massless spring with a force constant of $100\text{N/m}$ and is placed on a smooth horizontal surface. At $t=0$, a constant force of $F=10\text{N}$ is applied on the block, when the spring is in its natural length. The speed of the block, when it is displaced by $8\text{cm}$ from its mean position will be

1. $80\text{cm/s}$
2. $16\text{cm/s}$
3. $60\text{cm/s}$
4. $25\text{cm/s}$

Q.

If a cycle wheel of radius $0.5m$ completes one revolution in $1s$, then the acceleration of a point on the circumference of the wheel will be

1. $19.7m{s}^{-2}$

2. $10.7m{s}^{-2}$

3. $9.8m{s}^{-2}$

4. $14.2m{s}^{-2}$

Q. A particle moves along a straight line in such way that its accelertion is increasing at the rate of2 m/s3. If initial acceleration and initial velocity both were zero, thn find the dis†an ce covered by it in 3 seconds. (1) 27 m (2) 9 m

Q.

The instantaneous displacement of a simple harmonic oscillator is given by y = A cos (ωt + n/4). Its speed will be maximum at the time:

1. n/4ω

2. 2n/ω

3. ω/n

4. ω/2n

Q. A particle performing SHM has a velocity $v_0$ at mean position. Find the velocity of the particle, when it reaches a point which is at a distance $\frac{A}{2}$ from the mean position.
[$A=$ amplitude of SHM]

1. $\frac{v_0}{4}$
2. $\frac{\sqrt{3}}{2}{v}_0$
3. $\frac{3v_0}{2}$
4. $\frac{v_0}{\sqrt{2}}$

Q.

Mass A is connected with a string which passes through a fixed pulley. The other end of the string is connected with a movable pulley N. The block B is connected with another string which passes through the pulley N as shown in figure. Find the relation between acceleration of A & B.

1. 

2. 

3. 

4. 

Q. equation of trajectory of particle is y=3x -4x^{2. } acceleration is constnt 2 and directed along negative y axis. velocity when it passes through origi

Q. the velocity of a particle varies with position x as v = beta x^{-2n} where n and beta are cons†an ts. the acceleration of particle is

Q. The velocity of a bullet is reduced from 200m/s to100m/s while travelling through a wooden block of thickness 10cm. The retardation, assuming it to be uniform, will be

Q. Q. A particle travels 10m in first 5 seconds and 10m in next 3 seconds. Assuming constant acceleration, what is the distance travelled in next 2 seconds ? (1) 8.3m (2) 9.3m (3) 10.3m (4) None of these

Q. 107. A body travels 200cm in the first two seconds and 220cm in the next 4 sec with same acceleration. The velocity of the body at the end of the 7th second is

Q. Choose the correct option from (A), (B), (C) & (D) STATEMENT-1 : If instantaneous velocity of a particle is zero, then it can have instantaneous acceleration. STATEMENT-2 : Acceleration acting on a particle is independent of instantaneous state of the body. A) Statement-1 is true, Statement-2 is true, Statement-2 is a correct explanation for Statement-1 B) Statement-1 is true, Statement-2 is true, Statement-2 is NOT a correct explanation for Statement-1 C)Statement-1 is true but Statement-2 is false D)Statement-1 is false but Statement-2 is true

Q. The given graph shows the variation of velocity with displacement. Which one of the graph given below correctly represents the variation of acceleration with displacement ?

1. 
2. 
3. 
4. 

Q. A particle moves a dis†an ce x in time t according to equation x = (t + 5)–1. The acceleration of particle is proportional to (1) {(Velocity)}^{3/2 } (2) {(Dis†an ce)}^2 (3) {(Dis†an ce)}^{–2} (4) {(Velocity)}^{2/3}

Q.

A body starts from origin and moves along x - axis such that at any instant velocity is $v_t$ = 4 $t^3$ - 2t where t is in seconds $v_t$ is m $s^{-1}$ .

The acceleration of the particle when it is 2 m from the origin is 11 x m $s^{-1}$ , where x is

1. 3

2. 2

3. 7

4. 0

Q.

Derive the expression for the distance travelled in n^th second of a uniformly acceleratad motion.

Q. A particle Travels 10 m in first 5 seconds 10 m in next 3 seconds. assuming constant acceleration what is the distance travelled in next 2 seconds