A motor bike running at $90 \,km h ^{-1}$, is slowed down to $54 \,km h^{-1}$ by the application of brakes, over a distance of $40\, m$. If the brakes are applied with the same force, calculate $(i)$ total time in which bike comes to rest $(ii)$ total distance travelled by bike.
Case $1$ : $u=90 km h ^{-1}=(-) 25 ms ^{-1} ; v=54 km$
$h^{-1}=15 m \cdot s ^{-1} ; S =40 m ; a=?$
Applying $v^{2}-u^{2}=2 a S$
$(15)^{2}-(25)^{2}=2 \times a \times 40$
$80 a=-400$
$a=-5 m s ^{-2}$
Case $2$ : $u=90 km h ^{-1}=25 m s ^{-1} ; v=0 ; S =?$
$a=-5 m s ^{-2} ; t=?$
Applying $v^{2}-u^{2}=2 a S$
$(0)^{2}-(25)^{2}=2 \times(-5) \times S$
$S=\frac{-625}{-10}=62.5 m$
Applying $\quad v=u+a t$
$0=25-5 \times t$
or $5 t=25$ or $t=5 s$
The velocity-time graph of cars $A$ and $B$ which start from the same place and move along a straight road in the same direction is shown below
Calculate :
$(a)$ the acceleration of car $B$ between $2 \,s$ and $4\, s$.
$(b)$ the time at which both the cars have the same velocity.
$(c)$ the distance travelled by the two cars $A$ and $B$ in $8\, s$
$(d)$ Which of the two cars is ahead after $8\, s$ and by how much ?
The distance$-$time graph of a body is parallel to time axis. The body is
$(a)$ What is acceleration ? Write its $SI$ unit.
$(b)$ Draw velocity-time graph, when an object has
$(i)$ uniformly accelerated velocity
$(ii)$ uniformly retarded velocity.
A train $100 \,m$ long is moving with a velocity of $60\, km h^{-1}$. Find the time it takes to cross the bridge $1\, km$ long.
Out of the three speed$-$time graphs shown below
Identify the graph for the following cases.
$(i)$ A ball thrown vertically upwards and returning to the hand of the thrower ?
$(ii)$ A body decelerating to a constant speed and accelerating.