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A vehicle whose mass is $1200 kg$ is moving along a straight line with a uniform velocity of $90 km / h$ . By an unbalanced external force in $4 s$ its velocity is slowed down to $18 km / h$ . What will be the acceleration and change in momentum?

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- 5 m / s^{2} and - 24000 kg - m / s

- 4 m / s^{2} and - 12000 kg - m / s

- 5 m / s and - 12000 kg - m / s^{2}

- 4 m / s and - 12000 kg - m / s^{2}

answer is A.

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Detailed Solution

A vehicle whose mass is

1200 kg

is moving along a straight line with a uniform velocity of

90 km / h

. By an unbalanced external force in

4 s

its velocity is slowed down to

18 km / h

. The acceleration and change in momentum are

- 5 m / s^{2}

and

- 24000 kg - m / s

respectively.
Given:
Mass

(m) = 500 g = 0.5 kg

,
Velocity (Initial),

u = 90 km / h

= 90 \times (5 / 18) m / s

= 25 m / s

Velocity (Final),

v = 18 km / h

= 18 \times (5 / 18) m / s

= 5 m / s

Time,

t = 4 s

Acceleration of motorcar, a

= \frac{v - u}{t}

\Rightarrow a = \frac{5 - 25}{4}

\Rightarrow a = - \frac{20}{4}

\Rightarrow a = - 5 m s^{- 2}

(Here negative indicates decreasing velocity)

Change in momentum = (final  – initial) momentum

⇒

= mv - mu

= m (v - u)

= 1200 (5 - 25)

⇒

= 1200 \times (- 20)

Change in momentum = - 24000 kg - m / s

∴

Acceleration and change in momentum of the motorcar are

- 5 m / s^{2}

and

- 24000 kg - m / s

respectively.

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