Question 189: Motion in 2D & Vectors

Question

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

Accepted Answer

Velocity towards east direction,  $$\overrightarrow {{v_1}}  = 30\widehat i$$ m/s
Velocity towards north direction, $$\overrightarrow {{v_2}}  = 40\widehat j$$ m/s
Change in velocity, $$\Delta \overrightarrow v  = {\overrightarrow v _2} - {\overrightarrow v _1}$$ = $$\left( {40\widehat j - 30\widehat i} ight)$$
$$ 	herefore \left| {\Delta \overrightarrow v } ight| = \left| {40\widehat j - 30\widehat i} ight| = 50\,m/s$$
Average acceleration, $${\overrightarrow a _{av}}$$ = $${{change\,in\,velocity} \over {Time\, interval}}$$
$${\overrightarrow a _{av}} = {{{{\overrightarrow v }_2} - {{\overrightarrow v }_1}} \over {\Delta t}} = {{\Delta \overrightarrow v } \over {\Delta t}}$$
$$\left| {{{\overrightarrow a }_{av}}} ight| = {{\left| {\Delta \overrightarrow v } ight|} \over {\Delta t}} = {{50\,m/s} \over {10\,s}} = 5\,m/{s^2}$$

Answer

1 m/s
2

Answer

7 m/s
2

Answer

$$\sqrt 7 $$ m/s
2

Answer

5 m/s
2

Motion in 2D & Vectors

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

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