Answer

Verified

341.1k+ views

**Hint :**Acceleration is defined as: The rate of change of velocity with respect to time. Acceleration is a vector quantity as it has both magnitude and direction. It is also the second derivative of position with respect to time. OR It is the first derivative of velocity with respect to time.

Acceleration (a) $ =~\text{dv}/\text{dt} $

**Complete step by step solution:**

We have given, A graph of acceleration of particles as a function of time. We have to calculate the maximum speed of particles. Acceleration is defined as the rate of change of velocity with respect to time.

$ \text{a}=~\text{dv}/\text{dt} $

$ \text{dv}=\text{a}\times \text{dt} $

Taking integration on both sides

$ \int{dv}=a\int{dt} $ ------ (1)

Limit of integration Since, particle starts from rest (v=0) and, let maximum velocity is V and initial time is t = 0 and Time at which acceleration is maximum t = 2

i.e. $ \text{V}\to \text{0} $ to V

$ \text{t}\to \text{0} $ to 2

From eq. (1)

$ \int\limits_{0}^{V}{dv}=a\int\limits_{0}^{2}{dt} $

Acceleration is given by, a = 4

$ \left[ v \right]_{0}^{V}=4\left[ t \right]_{0}^{2} $

$ v-0=4\left[ 2-0 \right] $

$ V=8m{{s}^{-1}} $

Hence, maximum velocity is $ 8ms^{-1} $ .

**Note:**

Another method : Acceleration is given by

$ a=\dfrac{change\text{ }in\text{ }velocity}{time\text{ }taken} $

$ a=\dfrac{{{v}_{2}}-{{v}_{1}}}{{{t}_{2}}-{{t}_{1}}} $

From graph, (figure)

a = 4m/s2

$ \begin{align}

& {{v}_{2}}=Vm/s \\

& {{v}_{1}}=0 \\

& {{t}_{2}}=2,{{t}_{1}}=0 \\

& 4=\dfrac{V-0}{2-0} \\

& V=8m/s \\

\end{align} $

This is the maximum velocity /speed of a particle.

Recently Updated Pages

Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred

Basicity of sulphurous acid and sulphuric acid are

The branch of science which deals with nature and natural class 10 physics CBSE

What is the stopping potential when the metal with class 12 physics JEE_Main

The momentum of a photon is 2 times 10 16gm cmsec Its class 12 physics JEE_Main

How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Draw a diagram of nephron and explain its structur class 11 biology CBSE

What is the color of ferrous sulphate crystals? How does this color change after heating? Name the products formed on strongly heating ferrous sulphate crystals. What type of chemical reaction occurs in this type of change.

Write the difference between soap and detergent class 10 chemistry CBSE

Give 10 examples of unisexual and bisexual flowers

Differentiate between calcination and roasting class 11 chemistry CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

What is the difference between anaerobic aerobic respiration class 10 biology CBSE

a Why did Mendel choose pea plants for his experiments class 10 biology CBSE