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Acceleration

The position ...

Question

The position of a particle is given by
$r = 3.0 t^i + 2.0 t^{2}^j + 5.0 k$
where t is in seconds and the coefficients have the proper units for r to be the in metres.
(a) Find v(t) and a(t) of the particle.
(b) Find the magnitude and direction of v(t) at t =1.0 s.

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Solution

$r = 3 t^i + 2 t^{2}^j + 5^k$
On differentiation with respect to t
$v = 3^i + 4 t^j + 0^k$
On differentiation with respect to t
$a = 0^i + 4^j + 0^k$
At t=1 sec $v = 3^i + 4^j + 0^k$
Magnitude=5
tan $θ = \frac{4}{3}$

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Similar questions

r = 3.0 t^i - 2.0 t^{2}^j + 4.0^k m

r

v

a

The position of a particle is given by

Where t is in seconds and the coefficients have the proper units for r to be in metres.

(a) Find the v and a of the particle?

(b) What is the magnitude and direction of velocity of the particle at t = 2.0 s?

\to r

^i

t^{2}

^j

^k

¯ ¯ ¯ r = 3 t^{2}^ı + 3 t^ȷ + 4^k

t

¯ ¯ ¯ r

t = 2 s

\to r = 3 t^i + \sqrt{3} t^{2}^j - 4^k

t

\to r

\to v

t = \sqrt{3} s

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