Equations of Motion

A spacecraft is flying in a straight path and it has a velocity of $100 \mathrm{km} {\mathrm{s}}^{-1}$ fires its rocket motors for $8.0 \mathrm{s}$. At the end of this time, its velocity increases and becomes $140 \mathrm{km} {\mathrm{s}}^{-1}$ Find the distance travelled by the spacecraft in the first $12 \mathrm{s}$ after the motors were started? The motors were in action for only $8.0 \mathrm{s}$.

Derive all the three equations of motion from velocity-time graph.

When brakes are applied, the speed of a train decreases from $198 \mathrm{km} {\mathrm{h}}^{-1}$ to $90 \mathrm{km} {\mathrm{h}}^{-1}$ in $1000 \mathrm{m}$. How much further will the train move before coming to rest? (Assuming the retardation to be constant). Also find the time taken by the train to stop after the application of brakes. 

A bullet of mass $100 \mathrm{g}$ moving with an initial velocity of $200 \mathrm{m} {\mathrm{s}}^{-1}$, strikes a wooden block and comes to rest after penetrating a distance $4 \mathrm{cm}$ in it. Find the initial and final momentum of the bullet and also the retardation caused by the wooden block along with the resistive force exerted by the wooden block.

Throw light on significance of graphical representation of motion. List uses of graph. Derive third equation of motion graphically.

An object starts from rest and travels $20 \mathrm{m}$ in first $2 \mathrm{s}$ and $160 \mathrm{m}$ in next $4 \mathrm{s}$. Find its velocity $7 \mathrm{s}$ after the start.

Derive second equation of motion graphically.

A car accelerates from $8 \mathrm{m} {\mathrm{s}}^{-1}$ to $16 \mathrm{m} {\mathrm{s}}^{-1}$ in $10 \mathrm{s}$. Find its acceleration and displacement in this time.

A stone is dropped from a height of $20 \mathrm{m}$. Its velocity increases uniformly at $10 \mathrm{m} {\mathrm{s}}^{-2}$ during the fall. After how much time will it strike the ground and with what velocity will it strike?

List the three equations of motion. How will the equations change if the body is travelling with uniform velocity?

Derive a relation for distance travelled by uniformly accelerated body in interval between $6^{th}$ and $7^{th}$ second.

A racing car has uniform acceleration of $4 \mathrm{m} {\mathrm{s}}^{-2}$. What distance will it cover in $10 \mathrm{s}$ after the start?

An aeroplane starts from rest with an acceleration of $3 \mathrm{m} {\mathrm{s}}^{-2}$ and takes a run for $35 \mathrm{s}$ before taking off. What is the minimum length of runway and with what velocity the plane took off?

Shatabdi Express starts from rest and attains a velocity of $108 \mathrm{km} {\mathrm{h}}^{-1}$in $2 \mathrm{minutes}$. If acceleration is uniform, find acceleration and displacement of the train.

Derive third equation of motion graphically and mathematically obtain second equation of motion from it.

Derive second equation of motion mathematically.

An electron moving with a velocity of $5\times {10}^4 \mathrm{m} {\mathrm{s}}^{-1}$enters a uniform electric field and acquires a uniform acceleration of ${10}^4 \mathrm{m} {\mathrm{s}}^{-2}$ in the direction of motion. Find the time in which its velocity will be quadruple.

Draw a graph for a body in uniform acceleration form 'u' to 'v' for time 't'. Derive first equation of motion from the graph.

Derive the second equation of motion by graphical method.

A car retards uniformly at $5 \mathrm{m} {\mathrm{s}}^{-2}$ to stop after $4 \mathrm{s}$. Find the velocity at which it was travelling and distance covered before it stops.