2nd Equation of Motion

Q. A boy standing on a stationary lift (open from above) throws a ball upwards with the maximum initial speed he can, equal to 49 m s¯¹. How much time does the ball take to return to his hands? If the lift starts moving up with a uniform speed of 5 m s¯¹ and the boy again throws the ball up with the maximum speed he can, how long does the ball take to return to his hands ?

Q. If a particle is dropped from top of a tower, then ratio of times in falling first three successive equal { distances h is { (1) 1:2:3{ (2) 1:\sqrt2:\sqrt3{ (2) 1:\sqrt2:\sqrt3{ (3) 1:(\sqrt2-1):(\sqrt3-\sqrt2){ (4) 1:4:9

Q. A particle travels 10m in first 5 sec and 10m in next 3 sec. Assuming constant acceleration what is the distance travelled in next 2 sec ​

1. $8.3m$
2. $9.3m$
3. $10.3m$
4. None of above

Q. 211. A particle performs linear S.H.M. at a particularinstant, velocity of particle is u and acceleration isα while at another instant velocity of particle is v andacceleration is β (0 < α < β ). The distance betweenthe two positions is

Q.

Two particles move along x axis. the position of particle 1 is given by x = 6.00$t^2$ + 3.00t + 2.00 (in meters and seconds); the acceleration of particles 2 is given by a = -8.00t ( in meters per second squared and seconds) and, at t = 0, its velocity is 19 m/s. When the velocities of the particles match, what is their velocity?

1. 1

2. 2

3. 3

4. 4

Q. a body moving with uniform acceleration is having vel 2m/s and 8m/s at t=1 and t=4 .then avg vel of the particle in the given time interwal is

Q. 16. Point A on the rod AB has an acceleration of 5 m/s and a velocity of 6 m/s at an instant as shown in the figure. The acceleration of the end B at the same moment is:

Q.

The position x of a particle varies with time (t) as

x = at² - bt³

The acceleration of the particle will be zero at time

1. 

2. 

3. 

4. 

Q.

A particle experiences a constant acceleration for 20 sec after starting from rest. If it travels a distance $S_1$ in the first 10 sec and a distance $S_2$ in the next 10 sec, then

1. 

2. 

3. 

4. 

Q. Two trains A and B of length 400 m each are moving on two parallel tracks with a uniform speed of 72 km h¯¹ in the same direction, with A ahead of B. The driver of B decides to overtake A and accelerates by 1 m s¯². If after 50 s, the guard of B just brushes past the driver of A, what was the original distance between them ?

Q. 10.A body dropped from the top of a tower covers a distance 7x in last second of its journey where x is the distance covered in first second. How much time does it take to reach the ground?

Q. An object of mass $m$ is at rest on earth's surface. Escape speed of this object is $v_e$. Same object is orbiting earth with $h=R$, then its escape speed will be $v_e^{{}^{\prime }}$. Find the correct alternative

1. $v_e^{\prime }=\frac{\sqrt{2}{v}_e}{3}$
   
2. $v_e^{\prime }=\frac{v_e}{\sqrt{2}}$
   
3. $v_e^{{}^{\prime }}=2v_e$
   
4. $v_e^{{}^{\prime }}=\frac{v_e}{4}$
   

Q. The position x (in m) of a particle along a straight line is given as x=3t^2-18t. The maximum speed in the time interval t=0 to t=2s is

Q. pai21. For the one-dimensional motion of a particle, described by position x t +cost (where t is time ins and x is in m), the velocity of particle is zero at timetequals to(1) 0.3s(2) 1 s(3) 0.2s(4) 1.57 s

Q. Position, x (in metre) of a particle varies with time t (in second) as x(t) = 2 + 2t + t2 + t3. The ratio of magnitude of average velocity and magnitude of average acceleration of the particle for the time interval t = 1 s to t = 2 s is

Q. If two cars A and B start moving from the same point simultaneously have their positions varying with time t as and. Velocity of A w.r.t B, if their accelerations are equal, will be

Q. The position x of a particle with respect to time t along x-axis is given by x=9t∧2-t∧3 where x is in metres and t in seconds. What will be the position of this particle when it achieves maximum speed along the + x direction? (1) 24m (2) 32m (3) 54m (4) 81

Q. If a ball is thrown vertically upwards with speed $u$, the distance covered during the last $t$ seconds of its ascent is

1. $2g{t}^2$
2. $\frac{1}{2}g{t}^2$
3. $g{t}^2$
4. $\frac{3}{2}g{t}^2$

Q. The position of a projectile launched from the origin at t=0 is given byr=(40i + 50j)m at t=2s. If theprojectile was launched at an angle θ fromthe horizontal, then θ is (take g= 10 ms-2)(1) tan-1 2/3 (2)t an-1 3/2 (3) tan-17/4 (4) tan-1 4/5

Q. A body let fall from the top of a tower falls through 3/8 of its height during the last second of its fall.what is the height of tower

Q. The brakes applied to a bike produce retardation of $5{\text{m/s}}^2$. If the bike takes $4\text{s}$ to stop after the application of brakes, calculate the distance it travels during this time.

1. $40\text{m}$
2. $45\text{m}$
3. $35\text{m}$
4. $50\text{m}$

Q. A particle travels 10m in first 5 sec and 10m in next 3 sec. Assuming constant acceleration what is the distance travelled in next 2 sec ​

1. None of above
2. 
3. 
4. 

Q.

If a projectile is thrown with a velocity 10 ms^-1 at an angle of 30⁰ with the horizontal. Then the time of flight will be

1. 1 s

2. 2 s

3. 4 s

4. 3 s

Q. The position of a body moving along x axis at time t is given by -2t2 + t + 2 what is the average velocity of the body between t = 0 sec to t= 5 sec and instantaneous velocity of the body at t=5 seconds

Q. A stone that is thrown upwards is caught by the thrower himself after 10 seconds. What is the total distance travelled by the ball? (Neglect air friction and take $g=10m/s^2$)

1. $125m$
2. $250m$
3. $0m$
4. $200m$

Q.

The position x of a particle with respect to time t along x-axis is given by x = 9t² - t³ , where x is in meters and t in seconds. What will be the position of this particle when it achieves maximum speed along +x direction?

Q. Water drops are falling from a ceiling of height 5 m at a regular interval of 0.2 second. What is the speed of 3rd drop, when 1st drop just hitting the ground? (g 10 ms-2) (1) 4 ms-1 (3) 5 ms-1 (2) 6 ms- (4) 8 ms-1

Q. A cyclist starts from rest and moves with a constant acceleration of $1{\text{m/s}}^2$. A boy who is $48\text{m}$ behind the cyclist starts moving with a constant velocity of $10\text{m/s}$. After how much time the boy meets the cyclist? Choose the appropriate?

1. $8\text{s}$
2. $12\text{s}$
3. $10\text{s}$
4. both (1) and (2)

Q. A car is chasing a motorbike on a straight road. The car is going at its maximum speed $v$ (assumed uniform). The person on motorbike started his ride when the car was at a distance $d$ away from him, and the motorbike starts with constant acceleration $a$. What should be the condition for the speed of the car $v$, so that motorbike will be caught?

1. $v\le \sqrt{ad}$
2. $v\le \sqrt{2ad}$
3. $v\ge \sqrt{2ad}$
4. None of these

Q. A particle travels $10\text{m}$ in first $5\text{s}$ and $10\text{m}$ in next $3\text{s}$. Assuming constant acceleration what is the distance travelled in next 2 sec

1. $8.3\text{m}$
2. $9.3\text{m}$
3. $10.3\text{m}$
4. None of the above