Question 252: Laws of Motion

Question

An object of mass 3 kg is at rest. Now a force of $$\overrightarrow F $$ = 6t2 $$\widehat i$$ + 4t $$\widehat j$$ is applied on the object then velocity of object at t = 3 sec. is

Accepted Answer

Mass (m) = 3 kg, force (F) = $$6{t^2}\widehat i + 4t\widehat j$$
$$ 	herefore $$ acceleration
$$a = F/m = {{6{t^2}\widehat i + 4t\widehat j} \over 3} = 2{t^2}\widehat i + {4 \over 3}t\widehat j$$
Now, $$a = {{dv} \over {dt}} = 2{t^2}\widehat i + {4 \over 3}t\widehat j$$
$$dv = \left( {2{t^2}\widehat i + {4 \over 3}t\widehat j} ight)dt$$
$$ 	herefore v = \int\limits_0^3 {\left( {2{t^2}\widehat i + {4 \over 3}t\widehat j} ight)} dt$$
= $$\left. {{2 \over 3}{t^3}\widehat i + {4 \over 6}{t^2}\widehat j} ight|_0^3 = 18\widehat i + 6\widehat j$$

Answer

18$$\widehat i$$ + 3$$\widehat j$$

Answer

18$$\widehat i$$ + 6$$\widehat j$$

Answer

3$$\widehat i$$ + 18$$\widehat j$$

Answer

18$$\widehat i$$ + 4$$\widehat j$$

Laws of Motion

An object of mass 3 kg is at rest. Now a force of $\overrightarrow F = 6t2 \widehat i + 4t \widehat j$ is applied on the object then velocity of object at t = 3 sec. is

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