First slide

Circular motion

Question

A body is moving in a circle with a speed of 1 ms^-1. This speed increases at a constant rate of 2 ms^-1 every second. Assume that the radius of the circle described is 25 m.
The total acceleration of the body after 2 s is

Moderate

A

$2 {ms}^{- 2}$
B

$25 {ms}^{- 2}$
C

$\sqrt{5} {ms}^{- 2}$
D

$\sqrt{7} {ms}^{- 2}$

Solution

$\begin{array}{l} a_{t} = 2 {ms}^{- 2}, v = u + a_{t} t = 1 + 2 \times 2 = 5 {ms}^{- 1} \\ a_{c} = \frac{v^{2}}{r} = \frac{5^{2}}{25} = 1 {ms}^{- 2} \\ Net acceleration = \sqrt{a_{c}^{2} + a_{t}^{2}} = \sqrt{1^{2} + 2^{2}} = \sqrt{5} {ms}^{- 2} \end{array}$

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