Question

A particle has an initial velocity of $(3i + 4j)m{s^{ - 1}}$ and a constant acceleration of $(4i - 3j)m{s^{ - 2}}$. Its speed after one second will be equal to
A. $0m{s^{ - 1}}$
B. $7\sqrt 2 m{s^{ - 1}}$
C. $\sqrt {50} m{s^{ - 1}}$
D. $25m{s^{ - 1}}$

Answer 1

Hint:To get the solution of the above numerical we need to know the equation of motion. Apply Newton‘s first equation of motion in vector form such that we can calculate the speed after one second by substituting the values in the equation.

Formula used:
Newton‘s first equation of motion states that
$v = u + at$
Where, $v$ = final velocity of the particle, $u$ =initial velocity of the particle, $a$ = acceleration of the particle and $t$= time

Complete step by step solution:
Applying Newton‘s first equation of motion for $u = (3i + 4j)m{s^{ - 1}}$ ,$v = (4i - 3j)m{s^{ - 2}}$ at time $t = 1$ second, we get
$
v = (3i + 4j) + (4i - 3j) \times 1 \\
\Rightarrow v = 7i + j \\ $
The magnitude of the velocity will be in 1 second,
$
v = \sqrt {{7^2} + 1} \\
\Rightarrow v = \sqrt {49 + 1} \\
\therefore v = \sqrt {50} m{s^{ - 1}} \\ $
So the magnitude of the velocity of the particle is $\sqrt {50} m{s^{ - 1}}$.

Hence the correct option is C.

Additional information:
Commonly, the equations of motion which are used to describe the behavior of motion of an object as a function of time in a physical system. These equations of motions are differentiated were usually obtained by applying definitions of physical quantities which is used to set up an equation for the given problem.

Note: Do not use Newton‘s second equation of motion or Newton‘s third equation of motion as it can be done easily with the first equation itself and you will have to do very less calculation compared to other two methods. Also students should not get confused with the formulas of the equation of motion.