Equations of Motion by Graphical Method

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.

A ​motorboat starting from rest on a lake accelerates in a straight line at a constant rate of 3.0 m/s² for 8.0 s. How far does the boat travel during this time?

Mamta a student of class $\mathrm{X}$, while crossing the road in front of her school gate barely missed an accident. A car was going very fast from that road and as she was very alert, she had to respond very fast to avoid a hit from the car. She thought that had there been another student of class $\mathrm{V}$or so, probably the car would have hit that student. Next day she discussed this incident with her school principal and suggested to fix a sign board indicating speed limit and also for writing a letter to the municipal corporation to build speed bump before and after all the schools in her city.

$\left(iii\right)$ What values were displayed by Mamta?

Rohit wanted to go from place $\mathrm{A}$ to place $\mathrm{B}$. He had since travelled from $\mathrm{A}$to $\mathrm{B}$ through a highway which was too long. Rohit used Google maps to find a short way out so that he could save fuel and contribute less towards environmental pollution. He did find a shorter way and decided to travel through the shorter way.

Read the above passage and answer the following:

$\left(i\right)$What are the moral values shown by Rohit?

Namisha learnt to drive activa a few days back. She was challenged by a friend Deeksha to have a race from her house to school. Namisha accepted the challenge. Priyanka a friend of Namisha requested her to think once more before starting the race as, if unfortunately, she met an accident then it would not only be dangerous for her but also for some other persons whom she may hit.

After reading the above paragraph answer the following questions:

$\left(i\right)$ What are the moral values shown by Priyanka?

Priyanka was going through an article in newspaper. It was regarding precautions while driving. The article was as follows:

Are you dressed comfortably?

Are you wearing proper footwear?

Are you physically fit and mentally alert?

Are you relaxed and focussed on your driving?

Do you hear and see properly?

Are you free from effect of any medication or alcohol?

Do you wear a helmet while driving a two-wheeler?

Do you know the $2$ second rule? It means that there should be a $2$ second difference between two vehicles when they pass a stationary object on road side.

Do you keep the glasses and mirrors clean while driving?

Do you obey safe speed rules?

Do you use mobile phone while driving?

Do you have a medical first-aid box in your vehicle?

Do you park your vehicle in parking lots?

Do you sound horn if you are followed or feel danger?

Do you use extra caution in bad weather?

Do you check the tyre pressure, brake oil, engine oil, coolant and battery conditions time to time?

Priyanka got influenced and discussed whether she can put this article on the notice board? She got the nod and was happy to do so. She shared this article with her friends on facebook and through SMS.

Answer the following questions based on the above information:

$\left(b\right)$What is $2$ second rule?

A bus starting from rest moves with a uniform acceleration of $0.5 {\mathrm{ms}}^{-2}$ for $4$ minutes. The speed acquired by the bus in $4$ minutes is _____ ${\mathrm{ms}}^{-1}$.

Suppose a body starts with rest and accelerates at a rate of $2 \mathrm{m} {\mathrm{s}}^{-2}$, the time taken for the body to reach a speed of $8 \mathrm{m} {\mathrm{s}}^{-1}$ is :

A body at rest starts sliding from top of a smooth inclined plane and requires 4s to reach bottom. How much time does it take, starting from rest at top, to cover one-fourth of a distance?