a cyclist enters a curve at 28m radius at a speed of 16ms. he applies the brakes, and decreases his speed at a constant rate of 0.6ms. calculate the cyclist's centripetal radial and tangential accelerations when he is traveling at a speed of 13ms.

Answer 1

First, let's calculate the centripetal acceleration:

Centripetal acceleration $a_c=\frac{v^2}{r}$,
$a_c=\frac{(13ms{)}^2}{28m}$,
$a_c=\frac{169m{s}^2}{28m}$,
$a_c=6.04m{s}^2$.

Now, let's calculate the radial acceleration:

Radial acceleration $a_r=-\frac{dv}{dt}$,
Given that the cyclist is decreasing his speed at a constant rate of 0.6 ms,
$a_r=-0.6m{s}^{-2}$.

Lastly, let's calculate the tangential acceleration:

Tangential acceleration $a_t=\frac{dv}{dt}=-0.6m{s}^{-2}$.

Therefore, when the cyclist is traveling at a speed of 13ms, his centripetal acceleration is 6.04ms^2, his radial acceleration is -0.6ms^2, and his tangential acceleration is also -0.6ms^2.