Suppose we know velocity vector and acceleration vector. We can find component of accn along velocity by dot product How to find component of acceleration perpendicular to velocity?

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Q. A particle moves in such a way that its position vector at any time

t

\to r = t^i + \frac{1}{2} t^{2}^j + t^k

. Find as a function of time
(i) the velocity

(\begin{matrix} \frac{d \to r}{d t} \end{matrix})

(ii) the speed

(\begin{matrix} ∣ ∣ ∣ \begin{matrix} \frac{d \to r}{d t} \end{matrix} ∣ ∣ ∣ \end{matrix})

(iii) the acceleration

(\begin{matrix} \frac{d \to v}{d t} \end{matrix})

(iv) the magnitude of the acceleration
(v) the magnitude of the component of acceleration along velocity (called tangential acceleration)
(vi) the magnitude of the component of acceleration perpendicular to velocity (called normal acceleration).

Q. Assertion :In circular motion, dot product of velocity vector

(\to v)

and acceleration

(\to a)

may be positive, negative or zero. Reason: Dot product of angular velocity vector and linear velocity is always zero.

A particle moves along parabolic path y=2x-x²+2 in such a way that the x component of velocity vector remains constant(5m/s). Find the magnitude of acceleration of the particle.

Q. Assertion :In case of a projectile, the angle between velocity and acceleration changes from point to point. Reason: Because its horizontal component of velocity remains constant, while vertical component of velocity changes from point to point due to gravitational acceleration.

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