A truck running at $90\, km h ^{-1}$ is brought to rest over a distance of $25\, m$. Calculate the retardation and time for which brakes are applied.
$u=90 km h ^{-1}=25 m s ^{-1} ; v=0 ; S =25 m ; a=?$
$t=?$
$(i)$ Applying $v^{2}-u^{2}=2 a S$
$(0)^{2}-(25)^{2}=2 \times a \times 25$
$\Rightarrow$ $a=-\frac{625}{50}=-12.5 m s ^{-2}$
Therefore, retardation $=-a=12.5 m s ^{-2}$
$(ii)$ Applying $v=u+a t$
$0=25-12.5 \times t$
$12.5 t=25 \quad$ or $\quad t=2 s$
Name the physical quantities denoted by
$(i)$ The slope of the distance$-$time graph.
$(ii)$ The area under velocity$-$time graph.
$(iii)$ The slope of velocity$-$time graph.
Write true or false for the following statements
In one$-$dimensional motion, the average velocity and the instantaneous velocity are unequal.
The nelocitu$-$time graph of a body is as shown. What tupe of motion does the body posses ?
A particle accelerates from rest at a constant rate for sometime and attains a constant velocity of $8\, m s ^{-1}$. Afterwards it decelerates with a constant rate and comes to rest. If the total time taken is $4$ second, the distance travelled is
$(a)$ Define acceleration.
$(b)$ A stone describes a circular path with a constant speed. State the type of motion of the stone.