Kinematics - Differentiating Displacement and Velocity
Kinematics - Differentiating Displacement and Velocity
A particle starts from a fixed point \(A\) and travels in a straight line. The velocity, \(v\) m/s, of the particle, \(t\) s after leaving \(A\), is given by \(v = 2 + t - \sqrt{10t + 4}\).
- Find the acceleration of the particle when it is at instantaneous rest.
- Find the total distance travelled by the particle between \(t = 0\) s and \(t = 7\) s.
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Answer:(a) At \(t=0\), \(a=-\frac32\text{ m s}^{-2}\); at \(t=6\), \(a=\frac38\text{ m s}^{-2}\). (b) \(3.80\) m.
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