A particle moving with constant acceleration crosses x=0 at t=2 s and again at t=6 s. At t=4 s its position is -16 m. Its acceleration is:
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A particle moving with constant acceleration crosses x=0 at t=2 s and again at t=6 s. At t=4 s its position is −16 m. Its acceleration is:

G1 Physics · Accepted Answer

For constant acceleration, x(t) is quadratic. Since x=0 at t=2 and 6, x = K(t−2)(t−6). Comparing with x = x₀ + ut + (a/2)t², the coefficient K equals a/2. At t=4, −16 = K(2)(−2) ⇒ K=4. Therefore a=2K=8 m s⁻².