- #1
LukeEvans
- 22
- 0
A particle of mass m travels in a straight line and experiences a single force, F(t) , in the direction of motion that varies with time t.
( a ) Given that m = 6 kg and F( t ) = 6 sin t + 24 N, use Newton’s 2nd law to show that the acceleration, a m/s2 , of the particle is,
a = sin t + 4
( 2 marks )
( b ) Given that initially the particle starts from rest at a particular datum point on the line of motion, show that the distance traveled , x , from the datum point by the particle at time t is,
x = 2 t2 + t - sin t
Hence, show that the time taken for the particle to travel 8 m from the datum point is given by the solution of the equation f( t ) = 0 where
f( t ) = 2 t2 + t - 8 - sin t
( 4 marks )
The above is the question I'm struggling with. I have completed the first part (worth two marks) but included it for reference.
The result I got from the first part was (6 sin t + 24N)/6 = sin t + 4 m/s2.
The second part (worth four marks) has got me stumped. I would dearly love to see the steps taken to satisfy the question. Thank you.
( a ) Given that m = 6 kg and F( t ) = 6 sin t + 24 N, use Newton’s 2nd law to show that the acceleration, a m/s2 , of the particle is,
a = sin t + 4
( 2 marks )
( b ) Given that initially the particle starts from rest at a particular datum point on the line of motion, show that the distance traveled , x , from the datum point by the particle at time t is,
x = 2 t2 + t - sin t
Hence, show that the time taken for the particle to travel 8 m from the datum point is given by the solution of the equation f( t ) = 0 where
f( t ) = 2 t2 + t - 8 - sin t
( 4 marks )
The above is the question I'm struggling with. I have completed the first part (worth two marks) but included it for reference.
The result I got from the first part was (6 sin t + 24N)/6 = sin t + 4 m/s2.
The second part (worth four marks) has got me stumped. I would dearly love to see the steps taken to satisfy the question. Thank you.