Equations of Motion by Graphical Method

The initial velocity of a particle is $10 \mathrm{m}/\mathrm{s}$. It is moving with an acceleration of $4 \mathrm{m}/{\mathrm{s}}^2$. The distance covered by the particle after $2 \mathrm{s}$ is

Two bodies of masses $m_a, m_b\left(m_a> m_b\right)$ are dropped from heights $‘a’, ‘b’$respectively. The ratio of velocities with which they reach ground is:

A bus of mass $2800 \mathrm{kg}$ is travelling at a speed of $90 \raisebox{1ex}{$\mathrm{km}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{h}$}\right.$. A retarding force of $5600 \mathrm{N}$ is applied on it for a distance of $100 \mathrm{m}$. Its velocity reduces to

A stone is dropped into a well having free water surface at depth $44.1 \mathrm{m}$. The splash is heard $3.13 \sec$ after the stone is dropped. Find the velocity of sound in air (Take $g= 9.8 \raisebox{1ex}{$\mathrm{m}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{s}}^2$}\right.$)

A body is travelling with speed $20 \mathrm{m} {\mathrm{s}}^{-1}$ having acceleration $4 \mathrm{m} {\mathrm{s}}^{-2}$ the speed of the body after $2 \mathrm{s}$ is

A body is dropped from rest. Its velocity varies with displacement covered as: 

Three particles A, B and C are thrown from top of a building with same speed. A is thrown upwards, B is thrown downwards and C is thrown horizontally, they hit the ground with speed $V_A$, $V_{B }$and $V_C$ respectively then

Two steel balls of mass $1 \mathrm{kg}$ and $2 \mathrm{kg}$ and a lead ball of $10 \mathrm{kg}$ are released together from the top of tower $30 \mathrm{m}$ high. Assuming the path to be in vacuum:

The velocity – time graph of a moving body is shown in the figure. Which of the following statements is true?

Which of the following is an equation for position - Time relation?

A particle starts from origin O from rest and moves with an uniform acceleration along the positive x-axis. Identify all figures that correctly represent the motion qualitatively.

A body traveling along a straight line with a uniform acceleration has velocities $5$ m/s at a point A and $15$ m/s at a point B respectively. If M is the midpoint of AB, then

(i) The ratio of times taken by the body to cover distances MB and AM is $\left[\frac{\sqrt{5}-1}{2}\right]$.
(ii) The velocity at M is $5\sqrt{5}$ m/s.
(iii) The average velocity over AM is $\frac{5\left(\sqrt{5}+1\right)}{2}$m/s.
(iv) The product of the acceleration and the distance AB is $100m^2/s^2$.
Which of above statements are true?

A lift is going up. The variation in the speed of the lift is as given in the graph. What is the height to which the lift takes the passengers?

A stone is thrown vertically upward with a speed of u metres per second. A second stone is thrown vertically upward from the same point with the same initial speed but T seconds later than the first one. They collide at a distance of $\frac{\left({\mathrm{ku}}^2-{\mathrm{g}}^2{\mathrm{T}}^2\right)}{{\mathrm{K}}^{,}\mathrm{g}}$? metres above the point of $\frac{{\mathrm{K}}^{,}}{\mathrm{K}}$.projection. Then = ? 

A truck starts from rest and rolls down a hill with constant acceleration. It travels a distance of $400m$ in the $20s.$ Find its acceleration. Find the force acting on it if its mass is$7$ metric tons.

Study the following position—time graph of P, Q and R vehicles and compare their magnitude of displacements.

If a body is released from the top of a tower, the graph between distance $\left(\mathrm{x}\right)$ and time $\left(\mathrm{t}\right)$ is correctly shown by

Which of the following cannot be the speed (v)-time (t) graph?

If A and B starts from rest simultaneous with accelerations as mentioned in diagram.

Find how far from P, B overtakes A.

A stone is projected vertically upward with a speed of $15 m{s}^{-1}$ and one second later a second stone is projected vertically upward from the same point with the same speed. Find where the two stones meet.