Magnitude of Instantaneous Velocity

Q.

A body starts from the origin and moves along the X-axis such that the velocity at any instant is given by $(4t^3-2t)$, where t is in sec and velocity in m/s. What is the acceleration of the particle, when it is 2 m from the origin

1. 

2. 

3. 

4. 

Q.

The coordinates of a moving particle at any time are given by $x=a{t}^2$ and $y=b{t}^2$. The speed of the particle at any moment is

1. 

2. 

3. 

4. 

Q. A jet plane flying at a constant velocity v at a height = 8 km is tracked by a radar R located at O directly below the line of flight. If angle $\theta$ is decreasing at rate of 0.025 rad/s velocity of plane when $\theta$ = 60${}^{\circ }$ is

1. 
   1440 km/h
2. 
   480 km/h
3. 
   1920 km/h
4. 
   960 km/h

Q. Two cars P and Q starts from a point at the same time in a straight line and their positions are represented by $x_p\left(t\right)=at+b{t}^2$ and $x_Q\left(t\right)=ft-t^2$. At what time do the cars have the same velocity?

1. $\frac{f-a}{2(1+b)}$
2. $\frac{a-f}{1+b}$
3. $\frac{a+f}{2(b-1)}$
4. 
   $\frac{a+f}{2(1+b)}$

Q. Two cars P and Q starts from a point at the same time in a straight line and their positions are represented by $x_p\left(t\right)=at+b{t}^2$ and $x_Q\left(t\right)=ft-t^2$. At what time do the cars have the same velocity?

1. $\frac{f-a}{2(1+b)}$
2. 
   $\frac{a+f}{2(1+b)}$
3. $\frac{a-f}{1+b}$
4. $\frac{a+f}{2(b-1)}$

Q. Velocity of a particle as a function of time is shown in graph which is a parabola. If slope of the graph at $t=0$ is $2$ units and $v=p+qt+r{t}^2$, then (Assume SI units everywhere)

1. $q=4$
2. $r=-0.5$
3. $v_0=6m/s$
4. Velocity of particle is zero at $t=2\sqrt{3}+2$ sec

Q. The height y and the distance x along the horizontal plane of a projectile on a certain planet (with no surrounding atmosphere) are given by y = (8t - 5$t^2$)
meter and x=6t meter, where t is in second. The velocity with which the projectile is projected is

1. 8 m/sec
2. 6 m/sec
3. 10 m/sec
4. Not obtainable from the data

Q.

The coordinates of a moving particle at any time are given by $x=a{t}^2$ and $y=b{t}^2$. The speed of the particle at any moment is

1. 2t(a + b)

2. $2t\sqrt{(a^2-b^2)}$

3. $t\sqrt{(a^2+b^2)}$

4. $2t\sqrt{(a^2+b^2)}$

Q.

The coordinates of a moving particle at any time are given by $x=a{t}^2$ and $y=b{t}^2$. The speed of the particle at any moment is

1. 2t(a + b)

2. $2t\sqrt{(a^2-b^2)}$

3. $t\sqrt{(a^2+b^2)}$

4. $2t\sqrt{(a^2+b^2)}$