The graph given below is the distance$-$time graph of an object.
$(i)$ Find the speed of the object during first four seconds of its journey.
$(ii)$ How long was it stationary ?
$(iii)$ Does it represent a real situation ? Justify your answer.
$(i)$ $OP$ indicates uniform speed given
$v=\frac{75-0}{4-0}=\frac{75}{4}=18.75 m s ^{-1}$
$(ii)$ $PQ$ is parallel to the time axis. It indicates that the object is stationary. It is a real situation.
$(iii)$ $QR$ shows that distance and time decreases, which is not possible. Thus, this is not a real situation.
An electric train is moving with a velocity of $120\, km h^{-1} .$ How much distance will it corer in $30 \,s$ ?
A body thrown in the vertically upward direction rises upto a height $'h^{\prime}$ and comes back to the position of its start.
Calculate :
$(a)$ the total distance travelled by the body and
$(b)$ the displacement of the body. Under what condition will the magnitude of the displacement be equal to the distance travelled by an object ?
$(a)$ What is acceleration ? Write its $SI$ unit.
$(b)$ Draw velocity-time graph, when an object has
$(i)$ uniformly accelerated velocity
$(ii)$ uniformly retarded velocity.
The $v-t$ graph of cars $A$ and $B$ which start from the same place and move along straight road in the same direction, is shown. Calculate
$(i)$ the acceleration of car $A$ between $0$ and $8\, s$.
$(ii)$ the acceleration of car $B$ between $2\, s$ and $4\, s$.
$(iii)$ the points of time at which both the cars have the same velocity.
$(iv)$ which of the two cars is ahead after $8\, s$ and by how much ?
A piece of stone is thrown vertically upwards. It reaches its maximum height in $3$ second. If the acceleration of the stone be $9.8\, m s ^{-2}$ directed towards the ground, calculate the initial velocity of the stone with which it is thrown upwards. Find the maximum height attained by it.