Two stones are thrown vertically upwards simultaneously with their initial velocities $u _{1}$ and $u _{2}$ respectively. Prove that the heights reached by them would be in the ratio of $u_{1}^{2}: u_{2}^{2}$ (Assume upward acceleration is $-\,g$ and downward acceleration to be $+g$.
Can the distance travelled by a particle be zero when displacement is not zero ?
The velocity$-$time graph of a truck is plotted below
$(a)$ Calculate the magnitude of displacement of the truck in $15$ seconds.
$(b)$ During which part of the journey was the truck decelerating ?
$(c)$ Calculate the magnitude of average velocity of the truck.
What do uou understand by the term acceleration ? When is it positive and when is it negative ?
$(a)$ Derive second equation of motion $S=u t+\frac{1}{2} a t^{2}$ graphically where the symbols have their usual meanings.
$(b)$ A car accelerates uniformly from $18\, km h ^{-1}$ to $36\, km h^{-1}$ in $5$ seconds. Calculate the acceleration and the distance covered by the car in that time.