Question

a physics student monitors the speed and kinetic energy of a 0.49 kg traveling object. at a time of ( t = 1.0 , s ), the object is traveling with a speed of 7.5 m/s and at a time of ( t = 4.0 , s ), the object has a kinetic energy of 24 j. determine the following.
(a) the kinetic energy of the object (in j) at ( t = 1.0 , s )
j
(b) the speed of the object (in m/s) at ( t = 4.0 , s )
m/s

Explanation:

Step1: Calculate kinetic energy at \(t = 1.0\ s\)

The formula for kinetic energy is \(K=\frac{1}{2}mv^{2}\). Given \(m = 0.49\ kg\) and \(v=7.5\ m/s\).

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Step2: Calculate speed at \(t = 4.0\ s\)

We know \(K = 24\ J\) and \(K=\frac{1}{2}mv^{2}\). Rearranging for \(v\), we get \(v=\sqrt{\frac{2K}{m}}\). Substituting \(K = 24\ J\) and \(m=0.49\ kg\)

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Answer:

(a) \(13.78125\) J
(b) \(9.897\) m/s