Find the distance travelled by the space craft in the first $10 s$ after the rocket motors were started, the motors having been in action for only $6.0 s$ .

1000 k m

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1065 k m

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2000 k m

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None of these

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Solution

The correct option is C $1065 k m$
The space craft undergoes acceleration in first $6 s$ and moves with constant speed during last $4 s$ .
$u = 75 k m s^{- 1}$
$v = 120 k m s^{- 1}$
$t_{1} = 6 s$

This gives, $a = \frac{v - u}{t} = 7.5 k m s^{- 2}$
$∴ s_{1} = u t_{1} + \frac{1}{2} a t_{1}^{2} = (75 \times 6) + (\frac{1}{2} \times 7.5 \times 6^{2}) = 585 k m$
$t_{2} = (10 - t_{1}) = 4 s$
$∴ s_{2} = v \times t_{2} = (120 \times 4) k m = 480 k m$
$∴ s_{1} + s_{2} = (585 + 480) k m = 1065 k m$

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Find the distance travelled by the space craft in the first 10s after the rocket motors were started, the motors having been in action for only 6.0s.

Find the distance travelled by the space craft in the first $10 s$ after the rocket motors were started, the motors having been in action for only $6.0 s$ .