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# Differentiate y component of velocity wrt time

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1. A ball is thrown with an angle of 45 degrees to the horizontal by a person standing on the ground.

The y-component of the velocity of ball in projectile motion is differentiated with respect to time. i.e. dv/dt of the y-component of velocity.

Does this equal -g? (not g)
2. The y component the the balls vertical motion. On a speed-time graph the speed will start at the initial positive velocity, and be under constant deceleration ie, the graph declines with a straight line. As a=v/t, the gradient is it's acceleration, which is negative, so therefore -g.
3. (Original post by little pixie)
A ball is thrown with an angle of 45 degrees to the horizontal by a person standing on the ground.

The y-component of the velocity of ball in projectile motion is differentiated with respect to time. i.e. dv/dt of the y-component of velocity.

Does this equal -g? (not g)
The answer depends on your choice of the coordinate system.

If you choose the y-axis to point upwards, then dvy/dt = -g.

On the other hand, if you choose the y-axis to point downwards, then dvy/dt = g.

Most textbooks and exam questions take the y-axis to point upwards (it's simply a convention). So, in those instance, the acceleration in the y-direction is -g.

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