Physics for Scientists and Engineers 8th Edition Chapter 5 #70 Please provide me

Question

Physics for Scientists and Engineers 8th Edition Chapter 5 #70

Please provide me a complete step-by-step solutions! Thanks

The following is the problem:

A time-dependent force, F = (8.00i - 4.00tj), where F is in newtons and t is in seconds, is exerted on a 2.00 kg object initially at rest. (a) at what time will the object be moving with a speed of 15.0 m/s? (b) how far is the object from its initial position when its speed is 15.0 m/s ? (c) through what total displacement has the object traveled at this moment?

Explanation / Answer

The acceleration of the object v = u + at ==> v = at ==> a = v / t F = (8.00i - 4.00tj) magnitude |F| = 10 N (a) | F| = m a = m v / t ==> t = m v / F = 2 * 15 / 10 = 3.0 s (b) s = v^2 / 2 a = 15^2 / 2 * (15 / 3) = 225 / 2 * 5 = 22.5 m (c) m dv = (8.00i - 4.00tj) dt v = 4.00 t i - 1.00 t^2 j dx/dt = 4.00 t i - 1.00 t^2 j ==> x = 2.00 t^2 i - t^3 / 3 j = 2.00 * 3^2 i - 3^3 / 3 j = 18 i - 9 j

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