Question

A body with mass 5 kg is acted upon by a force F=(-3i+4j) N. If its initial velocity at t =0 is v =(6i-12j)msec^-1, the time at which it will just have a velocity along the y axis is
(1) never
(2)10sec
(3)2 sec
(4)15 sec

Answer 1

Answer on Question#49421 - Physics - Mechanics - Kinematics - Dynamics

A body with mass $m = 5 \, \mathrm{kg}$ is acted upon by a force $F = (-3i + 4j) \, \mathrm{N}$. If its initial velocity at $t = 0$ is $\pmb{v} = (6i - 12j)\frac{\mathrm{m}}{\mathrm{s}}$, the time at which it will just have a velocity along the y-axis is

(1) never

(2) 10 sec

(3) 2 sec

(4) 15 sec

Solution:

Let's consider the motion of the body along the x-axis. X-component of the force $F_{x} = -3 \, \mathrm{N}$ provides the body with acceleration $a_{x} = \frac{F_{x}}{m} = -0.6 \frac{\mathrm{m}}{\mathrm{s}^{2}}$. To find the $t$ at which the body moves with zero speed along the x-axis we'll use the following equation

$$v _ {x} ^ {f} = v _ {x} + a _ {x} t$$

where $v_{x}^{f}$ is the final velocity, $v_{x}$ is the initial velocity, $a_{x}$ is the acceleration, and $t$ is the time. Substituting $v_{x}^{f} = 0$ and $v_{x} = 6\frac{\mathrm{m}}{\mathrm{s}}$ into this equation we obtain

$$0 = 6 - 0.6 t \Rightarrow t = 10 \, \mathrm{s}$$

So, the correct answer is (2).

Answer: (2)

http://www.AssignmentExpert.com/