(a) At what time will the object be moving with a speed of 15.0 m/s? t = _______

Question

(a) At what time will the object be moving with a speed of 15.0 m/s?
t = _____________s

(b) How far is the object from its initial position when its speed is 15.0 m/s?
_________________ m

time-dependent force, = (7.95 ? 4.55t ), where is in newtons and t is in seconds, is exerted on a 2.00-kg object initially at rest. At what time will the object be moving with a speed of 15.0 m/s? At what time will the object be moving with a speed of 15.0 m/s? t = _____________s How far is the object from its initial position when its speed is 15.0 m/s? _________________ m Through what total displacement has the object traveled at this moment? ______________m

Explanation / Answer

The acceleration of the object   v = u + at, ==> v = at, ==> a = v / t

F = (8.00i - 4.00tj), magnitude |F| = sqrt(7.95^2 + 4.55^2 ) = 9.15 N

(a) | F| = m a = m v / t, ==> t = m v / F, = 2 * 15 /9.15,   = 3.27 s

(b) s = v^2 / 2 a,   = 15^2 / 2 * (15 / 3.27),   = 24.525 m

(c) m dv = (7.95 i - 4.55tj) dt,   v = 3.975 t i - 1.135 t^2 j,

dx/dt = 3.975 t i - 1.135 t^2 j

==> x = 1.98 t^2 i -0.37 t^3 j

= 2.00 * 3.27^2 i - 0.37* 3.27^3 / 3 j

= 21.38 i - 12.93 j

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