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The position vector of an object moving ...

The position vector of an object moving in X-Z plane is `vec(r)=v_(0)that(i)+a_(0)e^(b_(0)t)hat(k)`.
Find its (i) velocity `(vec(v)=(dvec(r))/(dt))` (ii) speed `(|vec(v)|)` (iii) Acceleration `((dvec(v))/(dt))` as a function of time.

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The correct Answer is:
(i) `vec(v)=v_(0) hat(i)+a_(0)b_(0)e^(b_(0)t)hat(k)` (ii) `|vec(v)|=sqrt(v_(0)^(2)+a_(0)^(2)b_(0)^(2)e^(2b_(0)t))` (iii) `vec(a)=a_(0)b_(0)^(2)e^(b_(0)t)hat(k)`
(i) `vec(v)=v_(0)hat(i)+a_(0)b_(0)e^(b_(0)t)hat(k)` (ii) `|vec(v)|=sqrt(v_(0)^(2)+a_(0)^(2)b_(0)^(2)e^(2b_(0)t))`
(iii) `vec(a)=a_(0)b_(0)^(2)e^(b_(0)t)hat(k)`
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