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AB is the velocity-time graph for motion of an object. What is the nature of this motion? Find the value of acceleration and total distance covered by the object.

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- 1.07 m s^{- 2}

;

45 m

- 2.08 m s^{- 2}

;

40 m

- 0.67 m s^{- 2}

;

48 m

- 1.07 m s^{- 2}

;

49 m

answer is C.

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Detailed Solution

The acceleration is

- 0.67 m s^{- 2}

and distance covered is

48 m

.
As we can see from the graph that the slope is negative, and motion is uniformly accelerated motion with negative slope.
Initial velocity,

u = 8 m s^{- 1}

Final velocity,

v = 0

Time,

t = 12 s

Calculation of acceleration,
By the first equation of motion,

v = u + at

Where,

v

= final velocity

u

= initial velocity

a

= acceleration

t

= time
Rearranging the above equation, we get
Acceleration,

a = \frac{v - u}{t}

\Rightarrow a = \frac{0 - 8}{12}

\Rightarrow a = - \frac{2}{3}

\Rightarrow a = - 0.67 m s^{- 2}

(Negative sign is indicating that the acceleration is decreasing or say retardation.)
Total distance covered by the object,

s =

Area of OAB

\Rightarrow s = \frac{1}{2} \times OA \times OB

\Rightarrow s = \frac{1}{2} \times 8 \times 12

\Rightarrow s = 48 m

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