A train starting from stationary position and moving with uniform acceleration attains a speed of 36 km/h in 10 minutes. Find the acceleration.
Answer
586.4k+ views
Hint : Uniform acceleration signifies that the acceleration is constant i.e. it does not change with time. All the values need to be calculated in the SI unit. So using the formula for the acceleration we can calculate its value by substituting the values of the velocity and time in the question.
Formula used: In this solution we will be using the following formula;
$ a = \dfrac{{v - u}}{{{t_2} - {t_1}}} $ , where $ a $ is the acceleration, $ v $ is the final velocity considered, $ u $ is the initial velocity, $ {t_1} $ is time at the initial velocity, and $ {t_2} $ is the time at the final velocity.
Complete step by step answer
When a moving body increases its velocity, it is said to have undergone acceleration. For our moving body in the question, it starts from rest and increases velocity to a certain amount under a particular time, hence it accelerates.
In mechanics, acceleration is fundamentally given by
$ a = \dfrac{{v - u}}{{{t_2} - {t_1}}} = \dfrac{{v - u}}{{\Delta t}} $ , where $ a $ is the acceleration, $ v $ is the final velocity considered, $ u $ is the initial velocity, $ {t_1} $ is time at the initial velocity, and $ {t_2} $ is the time at the final velocity.
Since, the train was stationary, initial velocity is zero. The final velocity considered is 36 km/h. and change in time is ten minutes.
Before proceeding, we must convert all given values to SI units.
$ v = 36\dfrac{{km}}{h} \times 1000\dfrac{m}{{km}} \times \dfrac{1}{{3600}}\dfrac{h}{s} = 10m/s $
$ \Delta t = 10\min \times 60\dfrac{s}{{\min }} = 600s $
Hence, by substituting into formula, the acceleration can be calculated as
$ a = \dfrac{{10 - 0}}{{600}} = \dfrac{1}{{60}} $
$ \Rightarrow a = 0.0167m/{s^2} $ .
Note
It is customary to write the formula for acceleration as
$ a = \dfrac{{v - u}}{t} $ , which can then be rearranged to be,
$ v = u + at $ which is called the first equation of motion.
For clarity, in this format, the time $ t $ signifies the time elapsed too, just like $ {t_2} - {t_1} = \Delta t $ . But, since only the time difference is considered, $ {t_1} $ can be considered a zero reference point and thus made zero as in $ {t_1} = 0 $ , and then $ {t_2} $ can just be called the time taken $ t $ from that time zero.
Formula used: In this solution we will be using the following formula;
$ a = \dfrac{{v - u}}{{{t_2} - {t_1}}} $ , where $ a $ is the acceleration, $ v $ is the final velocity considered, $ u $ is the initial velocity, $ {t_1} $ is time at the initial velocity, and $ {t_2} $ is the time at the final velocity.
Complete step by step answer
When a moving body increases its velocity, it is said to have undergone acceleration. For our moving body in the question, it starts from rest and increases velocity to a certain amount under a particular time, hence it accelerates.
In mechanics, acceleration is fundamentally given by
$ a = \dfrac{{v - u}}{{{t_2} - {t_1}}} = \dfrac{{v - u}}{{\Delta t}} $ , where $ a $ is the acceleration, $ v $ is the final velocity considered, $ u $ is the initial velocity, $ {t_1} $ is time at the initial velocity, and $ {t_2} $ is the time at the final velocity.
Since, the train was stationary, initial velocity is zero. The final velocity considered is 36 km/h. and change in time is ten minutes.
Before proceeding, we must convert all given values to SI units.
$ v = 36\dfrac{{km}}{h} \times 1000\dfrac{m}{{km}} \times \dfrac{1}{{3600}}\dfrac{h}{s} = 10m/s $
$ \Delta t = 10\min \times 60\dfrac{s}{{\min }} = 600s $
Hence, by substituting into formula, the acceleration can be calculated as
$ a = \dfrac{{10 - 0}}{{600}} = \dfrac{1}{{60}} $
$ \Rightarrow a = 0.0167m/{s^2} $ .
Note
It is customary to write the formula for acceleration as
$ a = \dfrac{{v - u}}{t} $ , which can then be rearranged to be,
$ v = u + at $ which is called the first equation of motion.
For clarity, in this format, the time $ t $ signifies the time elapsed too, just like $ {t_2} - {t_1} = \Delta t $ . But, since only the time difference is considered, $ {t_1} $ can be considered a zero reference point and thus made zero as in $ {t_1} = 0 $ , and then $ {t_2} $ can just be called the time taken $ t $ from that time zero.
Recently Updated Pages
If x a + bt + ct2 where x is in meters and t is in class 11 physics CBSE

A car covers the first half distance between two places class 11 physics CBSE

The resultant of two vectors overrightarrow P and overrightarrow class 11 physics CBSE

Find the value of cos 135 class 11 maths CBSE

A mass M is held in place by an applied force F and class 11 physics CBSE

A solution of glucose in water is labelled as 10 dfracwv class 11 chemistry CBSE

Trending doubts
One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

Simon Commission came to India in A 1927 B 1928 C 1929 class 11 social science CBSE

How are involuntary actions and reflex actions different class 11 biology CBSE

Earth rotates in which direction A East to west B West class 11 physics CBSE

Study of snakes is called A Herpetology B Ichthyology class 11 biology CBSE

What are polar and nonpolar solvents class 11 chemistry CBSE

