Derive the equation $v^{2}-u^{2}=2 a S$ graphically.
Derive the equation $v^{2}-u^{2}=2 a S$ graphically.
Consider the figure given below
Now, area of trapezium $OABD$
$=\frac{( OA + BD ) \times OD }{2}$
Now, $OA =u, BD =v,$ and $OD =t$
Therefore, we have
$S =\frac{(u+v) t}{2}$
or $S=\frac{(u+v)(v-u)}{2 a},$ using $v=u+a t$
Hence, we have
$v^{2}-u^{2}=2 a S$
Similar Questions
A motorcyclist drives from $A$ to $B$ with a uniform speed of $30\, km\, h^{-1}$ and returns back with a speed of $20 \,km \,h^{-1}$. Find its average speed(in $km\, h^{-1}$).
A motorcyclist drives from $A$ to $B$ with a uniform speed of $30\, km\, h^{-1}$ and returns back with a speed of $20 \,km \,h^{-1}$. Find its average speed(in $km\, h^{-1}$).
"The direction in which an object moves is given by the direction of velocity of the object and not by the direction of acceleration". Give an example to justify this statement
"The direction in which an object moves is given by the direction of velocity of the object and not by the direction of acceleration". Give an example to justify this statement
A particle is moving in a circular path of radius $r$. The displacement after half a circle would be :
A particle is moving in a circular path of radius $r$. The displacement after half a circle would be :
The velocity$-$time graph of a car is given below. The car weighs $1000\, kg$.
$(i)$ What is the distance travelled by the car in the first $2$ seconds ?
$(ii)$ What is the braking force at the end of $5$ seconds to bring the car to a stop within one second ?
The velocity$-$time graph of a car is given below. The car weighs $1000\, kg$.
$(i)$ What is the distance travelled by the car in the first $2$ seconds ?
$(ii)$ What is the braking force at the end of $5$ seconds to bring the car to a stop within one second ?
A motor bike running at $5\, m s ^{-1}$, picks up a velocity of $30\, m s ^{-1}$ in $5\, s$. Calculate $(i)$ acceleration $(ii)$ distance covered during acceleration.
A motor bike running at $5\, m s ^{-1}$, picks up a velocity of $30\, m s ^{-1}$ in $5\, s$. Calculate $(i)$ acceleration $(ii)$ distance covered during acceleration.