A particle is moving along x-axis. At time `t=0,` Its x-coordinate is `x=-4 m.` Its velocity-time equation is `v=8-2t` where, v is in m//s and t in seconds.
(a) At how many times, particle is at a distance of `8m` from the origin?
(b) Find those times.
A particle is moving along x-axis. At time `t=0,` Its x-coordinate is `x=-4 m.` Its velocity-time equation is `v=8-2t` where, v is in m//s and t in seconds.
(a) At how many times, particle is at a distance of `8m` from the origin?
(b) Find those times.
(a) At how many times, particle is at a distance of `8m` from the origin?
(b) Find those times.
Text Solution
Verified by Experts
The correct Answer is:
A, B, C, D
(a) Comparing the given v-t equation with `v=u+at.` we have,
`u=8 m//s` and
`a=-2 m//s^2=constant`
Now, motion of the particle is as shown below.
Now, `8m` distance from origin will be at two coordinates `x=8m and x=-8m.` From the diagram, we can see that particle will cross these two points three times, `t_1,t_2,and t_3.`
(b) `t_1` and `t_2`: At `x=8 m` displacement from the strating point is
`s=x_f-x_i=8-(4)=12 m`
Substituting in `s=ut+1/2 at^2,` we have
`12=8t-1/2xx2xxt^2`
Solving this equation, we get
smaller time `t_1=2s`
and larger time `t_2=6s`
`t_3`: At `x=-8m,` displacement from the starting point is
`s=x_f-x_i=-8-(-4)=-4 m`
Substituting in `s=ut+1/2at^2,` we have `-4=8t-1/2xx2xxt^2`
Solving this equation, we get the positive time,
`t_3=8.47s`
`u=8 m//s` and
`a=-2 m//s^2=constant`
Now, motion of the particle is as shown below.
Now, `8m` distance from origin will be at two coordinates `x=8m and x=-8m.` From the diagram, we can see that particle will cross these two points three times, `t_1,t_2,and t_3.`
(b) `t_1` and `t_2`: At `x=8 m` displacement from the strating point is
`s=x_f-x_i=8-(4)=12 m`
Substituting in `s=ut+1/2 at^2,` we have
`12=8t-1/2xx2xxt^2`
Solving this equation, we get
smaller time `t_1=2s`
and larger time `t_2=6s`
`t_3`: At `x=-8m,` displacement from the starting point is
`s=x_f-x_i=-8-(-4)=-4 m`
Substituting in `s=ut+1/2at^2,` we have `-4=8t-1/2xx2xxt^2`
Solving this equation, we get the positive time,
`t_3=8.47s`
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