Question

What is the speed of the body moving with uniform acceleration at the midpoint of two points on the straight line with the speeds are u and v

Answer 1

Let the total time be t seconds
We know that a=v-u/t
We know that v²=u²+2as
v²=u²+2×a×s/2
v²=u²+as
v=√u²+as

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Answer 2

we know ,

v = u + at 

a = v-u/t 

we get 

also ,

v² - u² = 2as 

v² = 2as + u²

v  = √( 2as + u²) 

put it in first equation we get 

√( 2as + u²)  = u + at 

2as + u² = u² + a²t² + 2uat 

2as = at(at + 2u) 

2s   = at² + 2ut 

s = at/2 + ut