Question

A force F → = 3i + 4j newton is applied on a body of mass 2 kg. Calculate the magnitude and direction of the acceleration in the body.

Answer 1

Magnitude of force =√{3^2+4^2}=√25=5
a=F/m=5/2m/s^2
the direction of acceleration is in the direction of force.

Answer 2

A force , $\vec{F}=3\hat{i}+4\hat{j}$ is applied on a body of mass 2kg.

according to Newton's 2nd law of motion,
rate of change of momentum per unit time is known as force.
e.g., $\vec{F}=m\vec{a}$

so, $3\hat{i}+4\hat{j}=2\vec{a}$

$\frac{1}{2}(3\hat{i}+4\hat{j})=\vec{a}$

$1.5\hat{i}+2\hat{j}=\vec{a}$

magnitude of a = $\sqrt{1.5^2+2^2}=2.5m/s^2$

direction of acceleration along direction of force [according to Newton's 2nd law of motion]