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" (3) Difference in "|(dvec v)/(dt)|" an...

" (3) Difference in "|(dvec v)/(dt)|" and "(d|vec v|)/(dt)?

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(a) What does |(dv)/(dt)| and (d|v|)/(dt) represent? (b) Can these be equal?

(a) What does |(dv)/(dt)| and (d|v|)/(dt) represent? (b) Can these be equal?

vec(r)=2that(i)+3tvec(2)hat(j) . Find vec(v) and vec(a) where vec(v)=(dvec(r))/(dr) , vec(a)=(dvec(v))/(dt)

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.

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.

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.

(i) What does |(dv)/(dt)| and (d|V|)/(dt) represent ? (ii) Can these be equal ? (iii) Can (d|V)/(dt)= 0 while |(dV)/(dt)ne0 ? (iv) Can (d|V|)/(dt)ne 0 while |(dv)/(dt)|=0 ?

(i) What does |(dv)/(dt)| and (d|V|)/(dt) represent ? (ii) Can these be equal ? (iii) Can (d|V)/(dt)= 0 while |(dV)/(dt)ne0 ? (iv) Can (d|V|)/(dt)ne 0 while |(dv)/(dt)|=0 ?

What does d|vec(v)|//dt and |d vec(v)//dt| represent ? Can these be equal ? Can. (a) d|vec(v)|//dt = 0 while |d vec(v)//dt| != 0 (b) d|vec(v)|//dt != 0 while |d vec(v)//dt| = 0 ?

A particle moves in such a way that its position vector at any time t is vec(r)=that(i)+1/2 t^(2)hat(j)+that(k) . Find as a function of time: (i) The velocity ((dvec(r))/(dt)) (ii) The speed (|(dvec(r))/(dt)|) (iii) The acceleration ((dvec(v))/(dt)) (iv) The magnitude of the acceleration (v) The magnitude of the component of acceleration along velocity (called tangential acceleration) (v) The magnitude of the component of acceleration perpendicular to velocity (called normal acceleration).