A proton moves rectilinearly. Its movement (its position) is governed by the following equation: x (t) = 7.8 + 9.2 t - 2.1 t^3, where t is expressed in s.
When does this proton reach its maximum position in x?
x(t) = 7.8 + 9.2t - 2.1t^3
differentiate with respect to t,
d(x(t))/dt = d/dt(7.8 + 9.2t - 2.1t^3)
v(t) = 9.2 - 6.3t^2
put v(t) = 0
9.2 - 6.3t^2 = 0
t^2 = 9.2/6.3
t^2 = 1.460
t = 1.21 s
differentiate v(t) with respect to t,
d/dt(v(t)) = d/dt(9.2 - 6.3t^2)
= -12.6t
At t = 1.21 s,
d/dt(v(t)) is negative,
So, t = 1.21 s gives maximum value of x(t)
Answer: 1.21 s
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