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| 1. |
Derive the formula s=ut + 1/2at^2 |
| Answer» Consider the linear motion of a body with an initial velocity u. Let the body accelerate uniformly and acquire\xa0a final velocity v after time t. The velocity–time graph is a straight line AB as shown below.\xa0At t = 0, initial velocity = u = OA\xa0At t = t, final velocity = v = OCThe distance S travelled in time t = area of the trapezium OABDs = (1/2)\xa0x\xa0(OA + DB) × ODs =\xa0(1/2)\xa0x\xa0(u + v) × t Since v = u + at,s =\xa0(1/2)\xa0x\xa0(u + u + at) × ts = ut +\xa0(1/2) at2 | |