Its question about velocity time graph?

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1 Answer
Apr 26, 2018

Magnitude of Frictional force acting on the block =0.12\ N.
We know that force of friction always opposes motion. As such when the block moves from X to Y. The frictional force produces a retardation. Which can be found from Newton's Second Law of Motion.

a=-F/m=(-0.12)/0.15=-0.8\ ms^-2

To find the velocity v of block when it hits Y can be found from the kinematic expression

v=u+at ........(1)

Inserting given values we get

v=3+(-0.8xx2)
v=1.4\ ms^-1 ......(2)

The block rebounds from the wall and moves directly towards X
before coming to rest at the point Z.

Kinetic energy as it his the wall =1/2mv^2=1/2xx0.15xx(1.4)^2
=0.147\ J
Kinetic energy lost on hitting the wall=0.072\ J.
Remaining kinetic energy on rebound=0.147-0.072=0.075\ J
Velocity v_r as it leaves Y on rebound can be found from

1/2mv_r^2=0.075
=>v_r=sqrt(2xx0.075/0.15)=+-1\ ms^-1
Selecting negative root as now the velocity is in opposite direction of initial velocity.
v_r=-1\ ms^-1 .......(3)

Time when block comes to rest at Z on rebound can be found from kinematic expression (1).
We note that after rebound magnitude of frictional force remains same but its direction changes. Hence we have

0=-1+0.8t
=>t=1/0.8=1.25\ s ......(4)

Once we have acceleration, velocity, and time we can sketch the velocity-time graph as shown below.

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