Question

The angular displacement of a body is a function of time and is given by equation: tither= 10 + 3t+ 6t^2, where t is in seconds.
Determine the angular velocity, displacement and acceleration when t = 5 seconds.

Answer 1

Angular velocity =

$\omega =\Delta\theta/\Delta t$

Differentiating $\Delta\theta$ with respect to $\Delta t$

we get $\omega = 3 +12\times t$

when t=5

$\omega =$ 3+12$\times t$ = 3 +12$\times 5 = 63 rad/s^2$

displacement

$\theta=10 +3\times t +6\times t^2$

when $t=5$

$\theta=10 +(5\times 5)+(6\times 5^{2})$

$\theta=10+25+150 =175 rad$

$Acceleration$$\alpha =\Delta\omega/\Delta t$

$Differentiating \Delta\omega$ $/\Delta t$

we get $\alpha =12 rad/s^{2}$