Velocity - time graph ? State how it can be used to find (i) acceleration of a body, (ii) displaceme

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7. MOTION

hard

What is velocity$-$time graph ? State how it can be used to find

$(i)$ the acceleration of a body,

$(ii)$ the displacement of the body,

$(iii)$ the distance travelled in a given time.

Option A

Option B

Option C

Option D

Solution

In the velocity-time graph, time is taken along the $x-$axis and velocity is taken along the $y-$ axis.

$(i)$ Since acceleration $=$ Change in velocity $/$ Time. Therefore, the slope of the velocitytime graph gives the acceleration. If the slope is positive, it is accelerated motion and if the slope is negative, the motion is retarded.

$(ii)$ Since velocity $\times$ time $=$ displacement. The area enclosed above the time axis represents positive displacement and the area enclosed below the time axis represents negative displacement. The total displacement is obtained by adding them numerically with proper sign.

$(iii)$ The total distance travelled by the body is their arithmetic sum (without sign).

Standard 9

Science

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 $.

medium

$(a)$ Define uniform circular motion.

$(b)$ Is the uniform circular motion an accelerated motion? Give reasons for your answer.

medium

Four cars $A$, $B$, $C$ and $D$ are moving on a levelled road. Their distance versus time graphs are shown in Fig. Choose the correct statement

medium

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 ?

medium

Derive the equation $v^{2}-u^{2}=2 a S$ graphically.

hard

What is velocity$-$time graph ? State how it can be used to find $(i)$ the acceleration of a body, $(ii)$ the displacement of the body, $(iii)$ the distance travelled in a given time.

Solution

Similar Questions

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 $.

$(a)$ Define uniform circular motion. $(b)$ Is the uniform circular motion an accelerated motion? Give reasons for your answer.

Four cars $A$, $B$, $C$ and $D$ are moving on a levelled road. Their distance versus time graphs are shown in Fig. Choose the correct statement

Derive the equation $v^{2}-u^{2}=2 a S$ graphically.

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What is velocity$-$time graph ? State how it can be used to find

$(i)$ the acceleration of a body,

$(ii)$ the displacement of the body,

$(iii)$ the distance travelled in a given time.

$(a)$ Define uniform circular motion.

$(b)$ Is the uniform circular motion an accelerated motion? Give reasons for your answer.