A body moves with a velocity of $2\, m s ^{-1}$ for $5\, s$ , then its velocity increases uniformly to $10\, m s ^{-1}$ in next $5\, s.$ Thereafter, its velocity begins to decrease at a uniform rate until it comes to rest after $5\, s$ .

$(i)$ Plot a velocity-time graph for the motion of the body.

$(ii)$ From the graph, find the total distance covered by the body after $2\, s$ and $12\, s$ .

Solution

$(ii)$ According to the graph :

Distance moved by the body after $2 s =$ Area $OAB ^{\prime} C ^{\prime}=2 m s ^{-1} \times 2 s =4 m$

Distance covered by the body after $12 s$

$=$ Area $OAED$ $+$ Area $BEF$ $+$ Area of $DHGI$ $+$ Area of $FHG$

$=2 m s ^{-1} \times 10 s +\frac{1}{2} \times 5 s \times 8 m s ^{-1}+$ $6 m s ^{-1} \times 2 s +\frac{1}{2} \times 2 s \times 5 m s ^{-1}$

$=20 m +20 m +12 m +4 m =56 m$

A satellite while revolving around the earth completes one revolution in $1$ hour and $30$ minutes. What is the angular speed of the satellite ?

Easy

Easy

Easy

Medium

Easy