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A ball is thrown at a relative velocity of $3 \ m/s$ in $+ve$ $x-$ direction in a rocket in gravity free space. The rocket has a constant acceleration of $2 m/s^2$ also in $+ve$ $x-$ direction.

My question :

Whether uniform acceleration equations of motion would apply in above case when using the rocket as a frame of reference. As an example, would the equation $s= ut + .5at^2$ apply if rocket is taken as frame of reference?

From my understanding the answer should be no since the above equation of motion can only be used when using an inertial frame of reference i.e. when frame of reference is moving at a constant velocity with respect to ground.

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    $\begingroup$ you can convert any non-intertial frame of reference into an intertial one with thw addition of a pseudo force on every body in that frame of reference. The pseudo force on a body of mass m in a frame accelerating with A is -mA. the minus sign indicates that the pseudo force is always opposite to the direction of the acceleration of the frame. $\endgroup$
    – Vulgar Mechanick
    Commented Dec 9, 2020 at 13:37
  • $\begingroup$ Then if we applied the equation of motion mentioned in question what would be values of u and a? I guess a would be in -ve x direction while u would 3m/s in +ve x direction. Or would a be 0. $\endgroup$
    – Sunil
    Commented Dec 9, 2020 at 13:43
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    $\begingroup$ @Sunil negative $\endgroup$
    – Linkin
    Commented Dec 9, 2020 at 13:46
  • $\begingroup$ @JustJohan, could you please mention the values of a and u including direction when using rocket as a frame of reference? $\endgroup$
    – Sunil
    Commented Dec 9, 2020 at 13:49
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    $\begingroup$ Yep. For an observer in an accelerated frame, you would have to apply pseudo force. $\endgroup$
    – Linkin
    Commented Dec 9, 2020 at 14:25

2 Answers 2

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Your understanding is correct, As said by overwatch in the comments you would have use fictitious forces to use Newton laws in non-inertial frames. You can read more about it here.

In your rocket example if we take the rocket as the reference frame it could be imagined as the rocket staying stationary and everything else moving/accelerating backward. So the ball will have retardation in the negative x-direction with respect to the rocket.

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  • $\begingroup$ But the value of u would still be in +ve direction when we use a pseudo force. Is that right? $\endgroup$
    – Sunil
    Commented Sep 15, 2022 at 6:39
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Earth itself is non-inertial frame of reference. The effects of rocket accelerating in space will be same as on earth with gravity equal to acceleration of rocket. Remember the case of elevators? and Einstein used this assertion to describe gravity.So yes, but be careful with some variables(such as time, distance travelled etc.) while calculation.

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