Third Equation of Motion

Q.

An object has a velocity $u$ at time $t=0$, it is undergoing retardation $a$ and covers a distance $s$ attaining a velocity $v$ in time $t$. Which of the following equations of motion correctly describe the motion?

1. $u=v-at$

2. $s=ut+\frac{1}{2}a{t}^2$

3. $u^2=2as+v^2$

4. $u=v+at$

Q.

A body with an initial velocity of $18\frac{km}{h}$ accelerates uniformly at the rate of $3\frac{cm}{s^2}$ over a distance of 200 m in $t$ s. What will be its be its velocity at time $t$?

1. $27\frac{m}{s}$

2. $37\frac{m}{s}$

3. $\sqrt{27}\frac{m}{s}$

4. $\sqrt{37}\frac{m}{s}$

Q. A car moving with an initial velocity 'u', brakes and stops. This implies the car is decelerating.

1. False
2. True

Q. If a body is thrown up with an initial velocity u and covers a height of h, then $h=\frac{u^2}{2g}$.

1. False
2. True

Q. A plane has a take-off speed of $120m{s}^{-1}$ after covering a distance of $2400m$. Determine the acceleration $\left(a\right)$ of the plane (assuming it to be constant) and the time $\left(t\right)$ required to reach that speed.

1. $a=4m{s}^{-2},t=30s$
2. $a=3m{s}^{-2},t=40s$
3. $a=3m{s}^{-2},t=30s$
4. $a=4m{s}^{-2},t=40s$

Q. An aeroplane accelerates from rest down a runaway at $3m{s}^{-2}$ for $30s$ until it finally lifts off the ground. Determine the distance travelled before take off.

1. $1350m$
2. $1620m$
3. $1700m$
4. $1482m$

Q. A body starts from point A with an initial velocity of $2m{s}^{-1}$ and with a constant acceleration of $\frac{5}{2}m{s}^{-2}$. How much distance would it have travelled when the velocity has reached $10m{s}^{-1}$?

1. $\frac{90}{5}m$
2. $\frac{92}{5}m$
3. $\frac{94}{5}m$
4. $\frac{96}{5}m$

Q. A body starts from point A with an initial velocity of $2m{s}^{-1}$ and with a constant acceleration of $\frac{5}{2}m{s}^{-2}$. How much distance would it have travelled when the velocity has reached $10m{s}^{-1}$?

1. $\frac{92}{5}m$
2. $\frac{90}{5}m$
3. $\frac{94}{5}m$
4. $\frac{96}{5}m$

Q.

A body when projected up with an initial velocity u goes to a maximum height h in time t and then comes back at the point of projection.The correct statement is:

(a) the average velocity is $\frac{2h}{t}$

(b) the acceleration is zero

(c) the final velocity on reaching the point of projection is 2u.

(d) the displacement is zero.

Q.

The driver of a train traveling at $40m{s}^{-1}$ applies the brakes as the train enters a station. The train slows down at a rate of $2m{s}^{-2}$. The distance traveled by train before stopping is

1. $200m$
2. $400m$
3. $300m$
4. $500m$