Question

A train is moving from one station to another in two hours’ time, its speed during the motion. The maximum acceleration during the journey. Also calculate distance covered during the time interval from $0.75hr$ to $1.00hr$.

Answer 1

Hint: In physics, acceleration is given as the rate of change of the velocity of an object with respect to the time. Acceleration is a vector quantity. The orientation of acceleration of an object is given by the orientation of the net force acting on that object.

Complete step by step answer:

First of all let us discuss the acceleration of an object in mechanics. The acceleration of a body is given as its variation in velocity over an increment of time. This can mean a variation in the speed of an object or its direction. Average acceleration is defined as the change of velocity happening over a period of time. Constant acceleration or the uniform acceleration is described when the velocity varies the same amount in every equal time period.
Here since acceleration is the rate of change of speed, it is expressed as the slope of the velocity time curve. Here the slope is largest in between $0.75hr$ and $1.00hr$ when we look into the graph.

Therefore the change in velocity is given as
$s=ut+\dfrac{1}{2}a{{t}^{2}}$ $=60-20km{{h}^{-1}}$
The acceleration in the interval $0.75hr$ to $1.00hr$ will be, change in velocity divided by change in time. That is,
 $\begin{align}
  & =\left( \dfrac{\left( 60-20 \right)km{{h}^{-1}}}{\left( 1-0.75 \right)h} \right)km{{h}^{-2}} \\
 & =160km{{h}^{-1}} \\
\end{align}$
Now let us find out the distance travelled,
Newton’s equation will give,
$s=ut+\dfrac{1}{2}a{{t}^{2}}$
Substituting the terms given in the question,
$\begin{align}
  & 20\times \dfrac{1}{4}+\dfrac{1}{2}\times 160\times {{\left( \dfrac{1}{4} \right)}^{2}} \\
 & =10km \\
\end{align}$
Hence the problem is solved.

Note:
There's no limit for acceleration since acceleration is dependable on the magnitude of the force resulting in the acceleration and the magnitude of the mass being accelerated. Newton's Second Law of Motion states that acceleration occurs when a force acts on a mass or an object. Riding your bicycle is a perfect example of this law of motion at work.