Question

a body moving with uniform acceleration passes two points A and B with velocities 20m/s and 30m/s respectively. find velocity midway

Answer 1

Let the the midpoint of AB be M and A and B are S m apart. Also, let acceleration of the body is A m/s²

Let velocity of body-

At A be U = 20 m/s

At B be V = 30 m/s

At C be W

For uniform acceleration motion, we know that

v² = u² + 2as

Now, here u = U, a = A, s = S, v = V.

Therefore, V² = U² + 2AS => S = (V² - U²)/2A—(1)

Now, for point M, s = S/2, u = U, v = W.

Therefore, W² = U² + 2A(S/2) => W² = U² + AS

Putting value of S in above equation from equation (1)—

W² = U² + A(V² - U²)/2A = U² + (V² - U²)/2

=> W² = (U² + V²)/2 => W =√(U²+V²)/2" role="presentation" style="margin: 0px; padding: 0px; outline: 0px; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">(U²+V²)/2(U²+V²)/2

Now, put the values

W² = (20²+30²)/2 = (400+900)/2 = 1300/2 =650

W = √650

Approx 25.5 m/s