$(a)$ 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.
Differentiate between distance and displacement.
The velocity-time graph (Fig.) shows the motion of a cyclist. Find $(i)$ its acceleration $(ii)$ its velocity and $(iii)$ the distance covered by the cyclist in $15\,\sec $.
A car is moving on a straight road with uniform acceleration. The following table gives the speed of the car at various instants of time.
Time $(s)$ | $0$ | $10$ | $20$ | $30$ | $40$ | $50$ |
Speed $\left(m s^{-1}\right)$ | $5$ | $10$ | $15$ | $20$ | $25$ | $30$ |
$(i)$ Draw the speed$-$time graph representing the above set of observations.
$(ii)$ Find the acceleration of the car.
The speed-time graphs of two cars are represented by $P$ and $Q$ as shown below
$(a)$ Find the difference in the distance travelled by the two cars (in $m$ ) after $4\, s$.
$(b)$ Do they ever move with the same speed ? If so when ?
$(c)$ What type of motion car $P$ and $Q$ are undergoing ?