First slide

The two types of acceleration

Question

A particle is moving along a circular path in xy-plane. When it crosses x-axis, it has an acceleration along the path of 1.5 m/s², and is moving with a speed of 10m/s in -ve y - direction. The total acceleration is

Moderate

A

$\large 50\hat i - 1.5\hat jm/{s^2}$
B

$10\hat i - 1.5\hat jm/{s^2}$
C

$- 50\hat i - 1.5\hat jm/{s^2}$
D

$1.5\hat i - 50\hat jm/{s^2}$

Solution

$\large \bar a_{net}=-a_c\hat i-a_t \hat j= \frac{-v^2}{r}\hat i-a_t \hat j=\frac{100}{2}\hat i-1.5 \hat j\\\\=(-50\hat i-1.5\hat j)ms^{-2}$

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