A 5.00-kg object passes through the origin at time t = 0 such that its x compone

Question

A 5.00-kg object passes through the origin at time t = 0 such that its x component of velocity is 5.00 m/s and its y component of velocity is -3.00 m/s.
(a) What is the kinetic energy of the object at this time?

(b) At a later time t = 2.00 s, the particle is located at x = 8.50 m and y = 5.00 m. What constant force acted on the object during this time interval?

(c) What is the speed of the particle at t = 2.00 s?

Explanation / Answer

m= 5.0 kg u = (5 i - 3j) m/s |u| = 5.830 m/s r = 8.50 i + 5.0 j |r| = 9.861 m (a) KE = 0.5 m |u|^2 = 0.5 * 5.0 * (5.830)^2 = 85 J (b) F * |r| = KE ==> F = KE / |r| = 85 / 9.861 = 8.619 N (c) acceleration a = F / m = 8.619 / 5 = 1.723 m/s^2 At t = 2 s, v = ? Using basic kinematic relation we have v = u + at = 5.830 + 1.723 * 2 = 9.277 m/s

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