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Home » A particle executes the motion described by x(t) = x0 (1 – e-γt) where t ≥ 0, x0 > 0 a) Where does the particles start and with what velocity? b) Find maximum and minimum values of x(t), v(t), a(t). Show that x(t) and a(t) increase with time and v(t) decreases with time.
A particle executes the motion described by x(t) = x0 (1 – e-γt) where t ≥ 0, x0 > 0 a) Where does the particles start and with what velocity? b) Find maximum and minimum values of x(t), v(t), a(t). Show that x(t) and a(t) increase with time and v(t) decreases with time.
CBSE | Class 11 | Motion in a straight line | NCERT Exemplar | Physics
A particle executes the motion described by x(t) = x0 (1 – e-γt) where t ≥ 0, x0 > 0 a) Where does the particles start and with what velocity? b) Find maximum and minimum values of x(t), v(t), a(t). Show that x(t) and a(t) increase with time and v(t) decreases with time.

a) x(t) = x0 (1 – e-γt)

v(t) = dx(t)/dt = +x0 γ e-γt

a(t) = dv/dt = x0 γ2 e-γt

v(0) = x0 γ

b) x(t) is minimum at t = 0 since t = 0 and [x(t)]min = 0

x(t) is maximum at t = ∞ since t = ∞ and [x(t)]max = e-γt = ∞

v(t) is maximum at t = 0 since t = 0 and v(0) = x0γ

v(t) is minimum at t = ∞ since t = ∞ and v(∞) = 0

a(t) is maximum at t = ∞ since t = ∞ and a(∞) = 0

a(t) is minimum at t = 0 since t = 0 and a(0) = -x0 γ2

i

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