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A body is moving with velocity 30 m/s towards east. After 10 seconds its velocity becomes 40 m/s towards north. The average acceleration of the body is
A
5 m/$s^2$
B
1 m/$s^2$
C
7 m/$s^2$
D
$\sqrt{7}$ m/$s^2$
Detailed Solution
Initial velocity $\vec{v_i} = 30\hat{i}$ m/s (east); final velocity $\vec{v_f} = 40\hat{j}$ m/s (north).
Change in velocity $\Delta\vec{v} = \vec{v_f} - \vec{v_i} = 40\hat{j} - 30\hat{i}$
$|\Delta\vec{v}| = \sqrt{40^2 + 30^2} = \sqrt{1600 + 900} = \sqrt{2500} = 50$ m/s
Average acceleration $= \frac{|\Delta\vec{v}|}{t} = \frac{50}{10}$
= 5 m/$s^2$
Change in velocity $\Delta\vec{v} = \vec{v_f} - \vec{v_i} = 40\hat{j} - 30\hat{i}$
$|\Delta\vec{v}| = \sqrt{40^2 + 30^2} = \sqrt{1600 + 900} = \sqrt{2500} = 50$ m/s
Average acceleration $= \frac{|\Delta\vec{v}|}{t} = \frac{50}{10}$
= 5 m/$s^2$