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 $\quad t=2 s$
A moving body is covering a distance directly proportional to the square of time. The acceleration of the body is
How can you find the following ?
$(i)$ Velocity from a displacement$-$time graph.
$(ii)$ Acceleration from velocity$-$time graph.
$(iii)$ Displacement from velocity$-$time graph.
$(iv)$ Velocity from acceleration$-$time graph.
The following displacement $-$ time graph shows the positions of a body at different times, Calculate the velocity of the body as it moves from : $(i) A-B \,(i i) B-C$ $(iii)$ $C-D$.
State which of the following situations are possible and give an example of each of these
$(a)$ A body moving with constant acceleration but with zero velocity.
$(b)$ A body moving horizontally with an acceleration in vertical direction.
$(c)$ A body moving with a constant velocity in an accelerated motion.
Velocity$-$time graph for the motion of an object in a straight path is a straight line parallel to the time axis.
$(a)$ Identify the nature of motion of the body.
$(b)$ Find the acceleration of the body.
$(c)$ Draw the shape of distance-time graph for this type of motion.