A frog hops along a straight line path from point $'A^{\prime}$ to point ${ }^{\prime} B ^{\prime}$ in $10\, s$ and then turns and hops to point ${ }^{\prime} C^{\prime}$ in another $5\, s$. Calculate the average speed and average velocity of the frog for the motion between $(a)(A)$ to $(B)(b)(A)$ to $(C)($ through $B)$
For $A$ to $B$, we have
Average speed $=$ Average velocity
$=\frac{(7-(-2))}{10}=0.9 m s ^{-1}$
For $A$ to $C$ through $B$, we have Average speed $=\frac{(7-(-2)+3-(-2))}{15}=\frac{14}{15} m s ^{-1}$
Average velocity $=\frac{(7-(3))}{15}=\frac{4}{15} m s ^{-1}$
The distance$-$time graph of a body is a straight line inclined to time axis. The body is in
Derive the equation $v^{2}-u^{2}=2 a S$ graphically.
Derive following equations for a uniformly accelerated motion
$(i)$ $v=u+a t$
$(ii)$ $S=u t+1 / 2 a t^{2}$
$(iii)$ $v^{2}-u^{2}=2 a S,$ where symbols have their usual meaning.
Following figure is the speed-time graph for a rocket from the moment when the fuel starts to burn, i.e. at time $t=0$.
$(a)$ State the acceleration of the rocket at $t=0$.
$(b)$ State what happens to the acceleration of the rocket between $t=5 s$ and $t=60 s$.
$(c)$ Calculate the acceleration of rocket at $t=80 s$ Give reason for your answer.
$(d)$ The total mass of the rocket at $t=80\, s$ is $1.6 \times 10^{6}\, kg .$ Calculate the resultant force on the rocket at this time. Give reason for your answer.
Write any two equations of motion for a body having uniform acceleration.