The displacement $x$ of a particle varies with time $t$ as $x = ae^{-\alpha t} + be^{\beta t}$, where $a, b, \alpha$ and $\beta$ are positive constants. The velocity of the particle will:

A ball is thrown vertically upwards. Which of the following plots represents the speed-time graph of the ball during its height if the air resistance is not ignored?

A body starts from rest. What is the ratio of the distance travelled by the body during the 4th and 3rd second?

The velocity of a bullet is reduced from $200 \text{ m/s}$ to $100 \text{ m/s}$ while travelling through a wooden block of thickness $10 \text{ cm}$. The retardation, assuming it to be uniform, will be:

A body A starts from rest with an acceleration $a_1$. After $2$ seconds, another body B starts from rest with an acceleration $a_2$. If they travel equal distances in the $5^{\text{th}}$ second, after the start of A, then the ratio $a_1 : a_2$ is equal to:

The displacement of a particle, moving in a straight line, is given by $s = 2t^2 + 2t + 4$ where $s$ is in metres and $t$ in seconds. The acceleration of the particle is:

A car moving with a velocity of $10 \text{ m/s}$ can be stopped by the application of a constant force $F$ in a distance of $20 \text{ m}$. If the velocity of the car is $30 \text{ m/s}$, it can be stopped by this force in:

Which of the following velocity-time graphs shows a realistic situation for a body in motion?

Time taken by an object falling from rest to cover the height of $h_1$ and $h_2$ is respectively $t_1$ and $t_2$. Then the ratio of $t_1$ to $t_2$ is: