A motor car slows down from $72\, km h ^{-1}$ to $36\, km h^{-1}$ over at distance of $25\, m$. If the brakes are applied with the same force calculate $(i)$ total time in which car comes to rest $(ii)$ distance travelled by it.
An object is moving along a straight line with uniform acceleration. The following table gives the velocity of the object at various instants of time
Time $(s)$ | $0$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ |
Velocity $\left( m s ^{-1}\right)$ | $2$ | $4$ | $6$ | $8$ | $10$ | $12$ | $14$ |
Plot the graph.
From the graph.
$(i)$ Find the velocity of the object at the end of $2.5 sec$
$(ii)$ Calculate the acceleration.
$(iii)$ Calculate' the distance covered in the last $4$ sec.
The velocity$-$time graph of a truck is plotted below
$(a)$ Calculate the magnitude of displacement of the truck in $15$ seconds.
$(b)$ During which part of the journey was the truck decelerating ?
$(c)$ Calculate the magnitude of average velocity of the truck.
A car manufacturer advertises that the brakes are so perfect that the car stops instantaneously. Comment.
Derive following equations for a uniformly accelerated motion
$(i)$ $v=u+a t$
$(ii)$ $S=u t+1 / 2 a t^{2}$
$(iii)$ $v^{2}-u^{2}=2 a S,$ where symbols have their usual meaning.