Acceleration in 2D

Q.

A body is traversing on the x-y plane with constant speed. At the start of the motion, the particles velocity is $40\hat{i}$ and after 30 sec its velocity becomes $40\hat{j}$. Find the average acceleration.

1. 

2. 

3. 

4. 

Q. The coordinates of a particle moving in a plane are given by x(t) = a cos (pt) and y(t) = b sin (pt) where a, b (<a) and p are positive constants of appropriate dimensions. Then

1. the velocity and acceleration of the particle are normal to each other at $t=\pi /\left(2p\right)$
2. the distance travelled by the particle in time interval $t=0tot=\pi /\left(2p\right)$ is a
3. the path of the particle is an ellipse
4. the acceleration of the particle is always directed towards a focus

Q. For an X-Y plot of a body undergoing 2D motion, the direction of instantaneous acceleration is always in the direction of change of velocities.

1. False
2. True

Q.
If A is the magnitude of the displacement covered by the particle from $t=4s$ to $t=7s$, B is the magnitude of the distance covered from from $t=4s$ to $t=7s$ and C is the magnitude of the final position of the particle w.r.t the origin, then A : B : C will be

1. 3 : 5 : 16
2. 3 : 5 : 15
3. 1 : 1 : 3
4. 5 : 5 : 16

Q.
Which of the following graphs correctly represents the position-time graph according to the given situation ?

1. 
2. 
3. 
4. 

Q. The coordinates of a moving particle at any time ${}^{\prime }{t}^{\prime }$ are given by $x=t^3$ and $y=4t^2$, where $x$ and $y$ are in metre and $t$ in second. The acceleration of the particle at time $t=1s$ is given by

1. $6{\text{ms}}^{-2}$
2. $8{\text{ms}}^{-2}$
3. $10{\text{ms}}^{-2}$
4. $14{\text{ms}}^{-2}$

Q. A particle moves along the parabolic path $x=y^2+2y+2$ in such a way that the $y-$ component of velocity vector remains $5{\text{ms}}^{-1}$ during the motion. The magnitude of the acceleration of the particle (in $m{s}^{-2}$) is

Q. A body traveling along a straight line traversed first one third of the total distance with a velocity $3\text{m/s}$. The remaining part of the distance was covered with a velocity $2\text{m/s}$ for half the time and with velocity $6\text{m/s}$ for the other half of time. The mean velocity over the whole time of motion is

1. $3.6\text{m/s}$
2. $5\text{m/s}$
3. $4.6\text{m/s}$
4. $4\text{m/s}$

Q. $\begin{array}{cc}\text{Column-I}& \text{Column-II}\\ \text{(i) For a particle moving in a circle}& \text{(a)}\text{The accleration may be perpendicular to its velocity}\\ \text{(ii) For a particle moving in a straight line}& \text{(b)}\text{The acceleration may be in the direction of velocity}\\ \text{(iii) For a particle undergoing projectile motion with angle of projection}\alpha ;0\le \alpha \le \frac{\pi }{2}& \text{(c)}\text{The acceleration may be at some angle}\\ & \theta (0\le \theta \le \frac{\pi }{2})\text{with the velocity}\\ \text{(iv) For a particle is moving in space}& \text{(d)}\text{The acceleration may be opposite to velocity}\end{array}$

1. i-a, b, ii-b, iii-a, c, iv-a, b, c, d
2. i-a, b, ii-b iii-a, c, iv-a, b, c, d
3. i-a, b, ii-b, d iii-a, c, iv-a, b, c, d
4. i-a, c, ii-b, d iii-a, c, iv-a, b, c, d

Q. A particle moves according to the law $a=-ky$. Find the velocity as a function of distance $y,v_0$ is initial velocity and particle is at origin initially.

1. $v^2=v_0^2-k{y}^2$
2. None
3. $v^2=v_0^2-2ky$
4. $v^2=v_0^2-2k{y}^2$