Answer:
Speed = 13.0m/s
Step-by-step explanation:
Given that velocity, v = (ai ± bj)m/s.
Because speed is scalar and has only magnitude, we can obtain it from the velocity by calculating only the magnitude given as:
[tex]Speed = (\sqrt{a^{2} + b^{2} } )m/s[/tex] ...Equation 1
From the question, we were given the position vector, r
The velocity can be obtained by differentiating r with respect to time, t
We have that differentiation of a constant is 0.
[tex]v = \frac{dr}{dt} = \frac{d}{dt}[(2.0+5.00t)i + (3.0 - 3.00t^{2})j] \\\\v = 0 + 5.00i + 0 - (6.00t)j[/tex]
At time t = 2.00s,
[tex]v = 5.00i - (6.00*2.00)j = 5.00i - 12.00j[/tex]
To obtain the speed, we use equation 1
[tex]Speed = \sqrt{(5.00)^{2} + (12.00)^{2} } = \sqrt{25 + 144} \\ \\Speed = \sqrt{169} = 13.00m/s[/tex]
Therefore, the speed of the object at time t = 2.00s is 13.00m/s
