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Please, Who Can Assist With The Solution To This Physics / Maths Problem by sureteeboy(m): 8:48am On Aug 12, 2020 |
A small particle moving with a uniform acceleration a, covers distances X and Y in the first two equal and consecutive intervals of time t. Show that a = (Y-X) / t² I tried simplifying this using the 3 equations of motion, but the answer I'm getting is quite different from what was required to prove Cc MrShape Femi4 Martinez39s |
Re: Please, Who Can Assist With The Solution To This Physics / Maths Problem by Martinez39s(m): 9:53am On Aug 12, 2020 |
Let the two equal time intervals for which the particle covered distances X and Y be [ t_{1} , t_{2} ] and [ t_{1} , t_{2} ] respectively. It follows that T = t_{2} - t_{1} = t_{3} - t_{2} ——— (1) The antiderivative of a(t) = a with respect to t is v(t) = at + C. C is the initial velocity. Since X is the distance traveled in the first interval, X is the definite integral of v(t) with respect to t from t_{1} to t_{2}. Similarly, Y is the definite integral of v(t) with respect to t from t_{2} to t_{3}. When you solve the integrals rightly using t_{1} , t_{2} , & t_{3} as the limits of integration, you have X = ½a(t_{2})² + Ct_{2} - ½a(t_{1})² - Ct_{1}. Y = ½a(t_{3})² + Ct_{3} - ½a(t_{2})² - Ct_{2}. We you solve Y - X and simplify using eq (1), you get Y - X = ¼a(t_{3} - t_{2})² = ¼a(2T)² _{NB: In your question, T is written as t.} 4 Likes |
Re: Please, Who Can Assist With The Solution To This Physics / Maths Problem by femi4: 10:16am On Aug 12, 2020 |
Solved 1 Like |
Re: Please, Who Can Assist With The Solution To This Physics / Maths Problem by Loris576(m): 10:16am On Aug 12, 2020 |
Nice one boss 1 Like |
Re: Please, Who Can Assist With The Solution To This Physics / Maths Problem by Loris576(m): 10:17am On Aug 12, 2020 |
Martinez39s:Nice Further conclude it 1 Like |
Re: Please, Who Can Assist With The Solution To This Physics / Maths Problem by peppo4live: 10:28am On Aug 12, 2020 |
Solution: distance (d1) = X distance (d2) = Y time = t1 = t2 = t (equal and consecutive intervals of time) initial velocity = d1/t = X/t final velocity = d2/t = Y/t Acceleration (a) = (final velocity - initial velocity)/t Putting X/t and Y/t into the formula for acceleration We have... Acceleration = (Y/t - X/t)/t Find the LCM inside the bracket We... (Y-X)/t ÷ t (Y-X)/t × 1/t Acceleration = (Y - X) / t² Proved and shown 4 Likes |
Re: Please, Who Can Assist With The Solution To This Physics / Maths Problem by Martinez39s(m): 10:38am On Aug 12, 2020 |
1 Like |
Re: Please, Who Can Assist With The Solution To This Physics / Maths Problem by Loris576(m): 10:40am On Aug 12, 2020 |
Martinez39s:a** 1 Like 1 Share |
Re: Please, Who Can Assist With The Solution To This Physics / Maths Problem by sureteeboy(m): 11:08am On Aug 12, 2020 |
Thanks very much everyone I was looking at the question from the wrong perspective |
Re: Please, Who Can Assist With The Solution To This Physics / Maths Problem by femi4: 12:08pm On Aug 12, 2020 |
peppo4live:I like this simple approach 3 Likes |
Re: Please, Who Can Assist With The Solution To This Physics / Maths Problem by peppo4live: 3:45pm On Aug 12, 2020 |
femi4: Thanks |
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