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  4. In U.C.M., when time interval δ tarrow0, the angle between change in velocity (δ v) and linear velocity (v) will be

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Q. In $U.C.M.$, when time interval $\delta t\rightarrow0$, the angle between change in velocity $(\delta v)$ and linear velocity $(v)$ will be

MHT CETMHT CET 2019

Solution:

The direction of change in velocity ($\delta v$) is given by
$\phi=\frac{180^{\circ}-\theta}{2}=90^{\circ}-\frac{\theta}{2} \,\,\,\,\,\,\, ...(i)$
This can be shown graphically as
image
For small time interval, i.e., $\delta t \rightarrow 0$, then angle between $v_{1}$ and $v_{2}$ is very small i.e., $\theta \approx 0^{\circ}$. So, from Eq. (i), we get
$\phi=90^{\circ}$