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This is second of our many quizzes on Speed and velocity. Click on this to access more such competitive quizzes on Mechanics.

Speed and velocity Quiz 2

physics

Which of the following statements are wrong ? $\\$ 1) Average speed is a vector quantity whereas average velocity is a scalar quantity. $\\$ 2) Average speed is a scalar quantity whereas average velocity is a vector quantity. $\\$ 3) Average speed as well as average velocity are vector quantities. $\\$ 4) Average speed as well as average velocity are scalar quantities.

The distance travelled is a scalar quantity and displacement is a vector quantity. 

  Average speed is the ratio of the total distance travelled by total time taken. Average velocity is the ratio of the total displacement by total time taken. As the distance travelled is a scalar quantity and displacement is a vector quantity.

The average velocity and average speed is similar to each other.Comment on this statement.  

 Average speed is the ratio of the total distance travelled by total time taken. Average velocity is the ratio of the total displacement by total time taken. 

  If the total displacement is equivalent to the total distance traversed in a particular time interval, then average velocity and the average speed will be similar. 

Rahul was participating in a running competition which is held in a circular track of $1\,km$.He participated in a $5\,km$ marathon and won the cup by completing it in $45\text{ s}$. What will be his average velocity and average speed respectively? 

Average speed is the ratio of the total distance travelled by total time taken. Average velocity is the ratio of the total displacement by total time taken. 

 $v=\dfrac{\text{distance}}{\text{time}} \\  \Rightarrow v=\dfrac{5\times {{10}^{3}}}{45} \\  \therefore v=111.11\,m{{s}^{-1}}\\ \text{Average velocity will be zero as the displacement will be zero.}\\ v=\dfrac{\text{displacement}}{\text{time}} \\  \therefore v=0\,m{{s}^{-1}}$

 Vinod is having a doubt regarding the velocity and speed.  He asked Pranav about whether the velocity or the speed will be greater. Pranav explained this in the form of a ratio and sorted out the issue.What will be the value of this ratio?  

The displacement always will be less than or equal to the distance travelled. 

 As we know velocity is the displacement divided by time and speed is the distance divided by time. The displacement always will be less than or equal to the distance travelled. Therefore, $\dfrac{v}{s}\le 1$.

Miri, a girl with $50\,kg$ mass, lost her energy of magnitude $20\,J$ as a dog ran behind her for a distance of $1\,km$. Find her velocity. 

Kinetic energy will be the half of the product of the mass and the square of velocity. 

 $\text{The energy can be found,}\\ KE=\dfrac{1}{2}m{{v}^{2}} \\  \Rightarrow v={{\left( \dfrac{2KE}{m} \right)}^{\dfrac{1}{2}}}\\ \text{Substituting the values,}\\ \Rightarrow v={{\left( \dfrac{2\times 20}{50} \right)}^{\dfrac{1}{2}}} \\  \therefore v={{\left( \dfrac{4}{5} \right)}^{\dfrac{1}{2}}} $