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# How to know if you should use s=1/2at^2 or s= ut + 1/2at^2?? watch

1. Hi, in some Physics questions the mark scheme simply uses s = 1/2at^2 instead of the whole s = ut + 1/2at^2 when u = 1.5

Here is an example question:

A coin is flicked off a table so that it initially leaves the table travelling in a horizontal direction with a speed of 1.5 m s –1 . The diagram shows the coin at the instant it leaves the table. Air resistance can be assumed to have a negligible effect throughout this question.

The table is 0.70 m high. Show that the coin takes approximately 0.4 s to reach the floor.

Answer in mark scheme:

0.7 m = 1/2(9.81 m s^-2 ) t^2
t = 0.37

They used s = 1/2at^2 here, why can't s = ut + 1/2at^2 be used??? Isn't the inital speed, u, 1.5???
2. This is a projectile motion question. In these questions, the motion is analysed in two distinct ways, horizontally and vertically.

Horizontally, u = 1.5 m s-1. Vertically, u = 0 m s-1.

In many questions of this type, the initial velocity is neither purely horizontal or vertical, but a mixture of both, in which case you would have to use components to find the horizontal and vertical u.

It is always a good idea in these questions to make separate lists of the s u v a t quantities for the horizontal and vertical motion, to avoid confusion.
3. (Original post by Stealth720)
Hi, in some Physics questions the mark scheme simply uses s = 1/2at^2 instead of the whole s = ut + 1/2at^2 when u = 1.5

Here is an example question:

A coin is flicked off a table so that it initially leaves the table travelling in a horizontal direction with a speed of 1.5 m s –1 . The diagram shows the coin at the instant it leaves the table. Air resistance can be assumed to have a negligible effect throughout this question.

The table is 0.70 m high. Show that the coin takes approximately 0.4 s to reach the floor.

Answer in mark scheme:

0.7 m = 1/2(9.81 m s^-2 ) t^2
t = 0.37

They used s = 1/2at^2 here, why can't s = ut + 1/2at^2 be used??? Isn't the inital speed, u, 1.5???
Because in this case the initial vertical velocity is zero.
4. Use s = ut + 0.5at^2 every time as practice, because you will get ut=0 if the initial velocity is 0 and it will work both ways then. The mark scheme is simply skipping a step.

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