Question

A particle is constrained to move in a circle with a 10-meter radius. At one instant, the particle's speed is 10 m/s and is increasing at a rate of $10m/s^2$. The angle between the particle's velocity and acceleration vectors is.

Answer 1

Tangential acceleration=$a_t=10m/s^2$

Radial acceleration$=a_r=\frac{v^2}{r}=\frac{{10}^2}{10}=10m/s^2$

Hence, $\tan \theta =\frac{a_r}{a_t}=1$

$⟹\theta ={45}^o$