The Equations of Motion

Q.

A body dropped freely from a height $\mathrm{h}$ onto a horizontal plane, bounces up and down, and finally comes to rest. The coefficient of restitution is $\mathrm{e}$, the ratio of distance traveled in two consecutive rebounds

1. $1:\mathrm{e}$

2. $\mathrm{e}:1$

3. ${\mathrm{e}}^2:1$

4. $1:{\mathrm{e}}^2$

Q.

During a practice match, a softball pitcher throws a ball whose height can be modeled by the equation h = $-16t^2$ + 24t + 1, where h = height in feet and t = time in seconds. How long does it take for the ball to reach a height of 6 feet?

1. 2.2, 3.8 secs

2. 5.4, 6.2 secs

3. 0.25, 1.25 secs

4. 7, 5 secs

Q. Why are the equations of motion applicable for the analysis of motion under gravity near the surface of the Earth? Assume terms have their usual meanings.

1. ‘g’ is constant near the earth's surface.
2. ‘g’ varies near the earth's surface.
3. ‘G’ is constant varies near the earth's surface.
4. ‘G’ is constant near the earth's surface.

Q. The logarithm of $27$ to the base $9$ is $\frac{3}{m}$. Then the value of $m$ is equal to

1. $0$
2. $2$
3. $3$
4. $6$

Q.

The kinetic energy acquired by the body of mass $m$after traveling a fixed distance from rest under the action of a constant force is

1. directly proportional to mass $m$

2. inversely proportional to mass $m$

3. inversely proportional to mass $m^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$

4. independent of mass $m$

Q. Solve $\frac{\frac{1}{2}÷4+20}{\frac{1}{2}\times 4+20}=?$

Q.

A stone thrown upwards with a speed of 20 metres per second loses speed at the rate of 9.8 metres every second. Find an algebraic expression which gives the speed of the stone at various times.