First slide

The two types of acceleration

Question

A particle is moving with a velocity of $\vec{v} = (3 \hat{i} + 4 t \hat{j})$ m/s. Find the ratio of tangential acceleration to that of normal acceleration at t= 1sec.

Moderate

A

4/3
B

3/4
C

5/3
D

3/5

Solution

$At t=1s,v= \sqrt{3^{2} + 4^{2}} = 5, \vec{a} = \frac{d \vec{v}}{dt} = 4 \hat{j}$
$\begin{array}{l} a_{t} = 4 \cos 37^{\circ} = \frac{16}{5}, a_{N} = 4 \sin 37^{\circ} = \frac{12}{5} \\ \Rightarrow \frac{a_{t}}{a_{N}} = \frac{16}{12} = \frac{4}{3} \end{array}$

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