Motion Under Variable Acceleration

Q.

The velocity of a particle moving along a straight line increases according to the linear law v = $v_0$ + kx

where k is a constant . Then

1) the accelearation of the particle is k($v_0$ + kx)

2) the particle takes a time $\frac{1}{k}$ $lo{g}_e$ ($\frac{v_1}{v_0}$) to attain a velocity $v_1$

3) velocity varies linearly with displacement with slope of velocity displacement curve equal to k

4) data is insufficient to arrive at a conclusion.

1. 1, 2, 3 are correct

2. 2, 3 are correct

3. all of them are correct

4. 1 and 2 are correct

Q.

A particle located at x = 0, at time t = 0 starts moving along the positive x direction with a velocity v that varies as v = $\alpha$ $\sqrt{x}$.The displacement of the particle varies with time as

1. t

2. t²

3. t^1/2

4. t³

Q.

What if I wanted the displacement and distance of a body between times t = 0 and time t = 5 for $V\left(t\right)=4-t^2$

1. None of these

2. displacement= -21.666, distance = 32.333

3. displacement= 32.333, distance = -21.666

4. displacement= 21.666, distance = 32.333

Q.

A particle moves according to the equation $\frac{dv}{dt}$ = $\alpha$ - $\beta$ v , where $\alpha$ and $\beta$ are constants. Find the velocity as a funtion of time. Assume body starts from rest.

1. 

2. 

3. 

4. 

Q.

If the speedometer of a bike riding along a straight road varies with time as given $v\left(t\right)=(t+3{)}^2+t^2$ What will be its accelaration at time t = 1s.

1. None of these

2. 10

3. 5

4. -10

Q.

A particle is moving along the path given by y = $\frac{c}{6}$ $t^6$(where c is positive constant). The relation between the acceleration (a) and the velocity (v) of the particle at t=5 sec. Is

1. 

2. 

3. 

4. a =

Q. The position of a particle moving in the xy-plane at any time is given by $x=(3t^2-6t)$ metres, $y=(t^2-2t)$ metres. Select the correct statement about the moving particle from the following

1. The velocity of the particle is zero at t = 1 second
2. The velocity and acceleration of the particle are never zero
3. The acceleration of the particle is zero at t = 0 second
4. The velocity of the particle is zero at t = 0 second

Q.

A particle moving in a straight line has velocity and displacement equation as V = 4 $\sqrt{1+S}$ , where V in m/s and s is in m.

The initial velocity of the particle in m/s is ______

1. 4

2. 9

3. 8

4. 7

Q.

If the speedometer(in km/h) of a bike riding along a straight road varies with time as given \(V(t) = 3t^2\)

What will be the distance it has covered after time t = 2 hr?

__

Q.

A ball is dropped on the floor from a height of 10 m. It rebounds to a height of 2.5 m. If the ball is in contact with the floor for 0.01 sec, the average acceleration during contact is

1. 

2. 

3. 

4.