J J Science Academy
1. A particle moves in a straight line and its position x at time t is given by $x=2+t$. Its velocity is
2. The displacement ' x ' (in meter) of a particle of mass ' m ' (in kg ) moving in one dimension under the action of a force is released to time ' t ' (in sec) by $t=\sqrt{x}+3$. The displacement of the particle, when its velocity is zero will be
3. The distance travelled by the particle along X -axis from 0 , is given by, $x=70+64 t-2 t^4$. It comes to rest at time $t=$
4. The motion of a particle is described by the equation, $x=a+bt^2$ where $a=15 \text{ cm/s}^2$ and $b=3 \text{ cm/s}^2$. Its instantaneous velocity at time 3 sec will be
5. A particle is moving in a straight line such that is displacement is given by, $s=\frac{t^4}{4}-2 t^3+6 t^2+15$, where $s$ is in metre and $t$ in second. The average acceleration during time interval $t=0$ to $t=4 \text{ s}$ is
6. The displacement $x$ of a particle along a straight line at time $t$ is given by, $x=2+3 t+5 t^2$. The acceleration of the particle at $t=2 \text{ s}$ is
7. A particle is moving along x -axis such that velocity and displacement are related as $v=\alpha x^{1/2}$, the acceleration of particle will be
8. If $v$ is the velocity of a body moving along $x$-axis is $v=-2 t^2+t-3$, then acceleration of body at $t=4 \text{ s}$, is
9. The displacement ' x ' of a particle at any instant is related to its velocity as, $v=\sqrt{2 x+9}$. Its acceleration is
10. The equation of motion of a body is given by, $x=t^3-3 t^2+12$. Its acceleration, at the beginning, is
11. The position $x$ of a body as a function of time $t$ is given by the equation, $x=2 t^3-12 t^2+24 t+6$. The direction of motion of the body changes at $t=$
12. A particle moves a distance x in time t according to equation $x=(t+5)^{-1}$. The acceleration of particle is proportional to
13. A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to $v(x)=\beta x^{-2n}$, where $\beta$ and $n$ are constants and $x$ is the position of the particle. The acceleration of the particle as a function of $x$ is given by
14. A particle moves in a straight line, its position (in m ) as function of time is given by $x=(at)^2+b$. What is average velocity in time interval $t=3 \text{ sec}$ to $t=5 \text{ sec}$? (where $a$ and $b$ are constants and $a=1 \text{ m/s}^2, b=1 \text{ m}$)
15. The position of a particle moving on x -axis is given by, $x=At^3+Bt^2+Ct+D$. The numerical value of $A, B, C, D$ are $1,4,-2$ and $5$ respectively and S.I. units are used. What is the velocity of the particle at $t=4 \text{ s}$?
16. A particle is moving in a straight line under retardation $a=\lambda v$, where $\lambda$ is constant. If $v_0$ is the initial velocity, after how much time the velocity of particle will be $v_0/4$?
17. The acceleration a (in $ms^{-2}$ ) of a body, starting from rest varies with time t (in s) following the equation, $a=3 t+4$. The velocity of the body at time $t=2 \text{ s}$ will be
18. If the velocity of a particle is $v=At+Bt^2$, where A and B are constants, then the distance travelled by it between $1 \text{ s}$ and $2 \text{ s}$ is
19. A particle starts from rest. Its acceleration (a) versus time (t) graph is as shown in the figure. The maximum speed of the particle will be
