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M1 questions

I need to check wether i did them correctly,so thanks for any help

here are the questions

1. The top of an inclined plane is at a height of .7m above the bottom.A block of mass .2kg is released from rest at the top of the plane and slides a distance of 2.5m to the bottem.Find the kinetic energy of the block when it reaches the bottem of the plane in each of the following cases:
a) the plane is smooth
b)the coeffecient of friction between the plane and the block is 0.15?

2. A particle P moves in a straight line that passes through teh origin O. The velocity of P at tiem t seconds is v ms^-1, where v=20t-t^3. At time t=0 the particle is at rest at a point whose displacement from O is -36m.
a) Find an expression for the displacement of P from O in terms of t.
b) Find the displacement of P from O when t=4.
c) Find the values of t or which the particle is at ).

3. A car of masss 1200kg travels along a horizontal straight road.The power of the car's engine is 20KW.The resistance to the car's motion is 400N.
a) Find the speed of the car at an instant when its acceleration is 0.5ms^-1.
b) Show that the maximum possible speed of the car is 50ms^-1.

The work done by the car's engine as the car travels from point A to point B is 1500KJ.
c) Given that the car is travelling at its max possible speed between A and B find the time taken to travel from A to B.

4. A particle P1 is projected vertically upwards,from a horizontal ground with a speed of 30ms^-1. At the same instant another particle P2 is projected vertically upwards from the top of a tower of height 25m with a speed of 10ms^-1. Fin
a) the time for which P1 is higher than the top of the tower.
b) the velocities of the partickes at the instant when the particles are at the same height.
c) the time for which P1 is higher than P2 and is moving upwards.

Reply 1

yazan_l

1. The top of an inclined plane is at a height of .7m above the bottom.A block of mass .2kg is released from rest at the top of the plane and slides a distance of 2.5m to the bottem.Find the kinetic energy of the block when it reaches the bottem of the plane in each of the following cases:
a) the plane is smooth
b)the coeffecient of friction between the plane and the block is 0.15?

using conservation of energy:
a)
K.E.gained = P.E.lost
K.E. = m g h
K.E. = 0.3 x 9.8 x 0.7 = 2.06 J

b) ΔK.E. + ΔP.E. = Work External
ΔK.E. + ΔP.E. = -friction x distance
K.E. - m g h = -0.15 x m g cos@ x 2.5
K.E. = 2.06 - 0.15 x 0.3 x 9.8 x 24/25 x 2.5
K.E. = 2.06 - 1.06 = 1 J (3 S.F.)

Reply 2

yusufu

Salman

2. A particle P moves in a straight line that passes through teh origin O. The velocity of P at tiem t seconds is v ms^-1, where v=20t-t^3. At time t=0 the particle is at rest at a point whose displacement from O is -36m.
a) Find an expression for the displacement of P from O in terms of t.
b) Find the displacement of P from O when t=4.
c) Find the values of t or which the particle is at ).

a) s= 10t^2 - (t^4)/4 - 36
b) s = 10(16) - (256)/4 - 36 = 160 - 64 - 36 = 60m
c) where is the particle?

Salman

3. A car of masss 1200kg travels along a horizontal straight road.The power of the car's engine is 20KW.The resistance to the car's motion is 400N.
a) Find the speed of the car at an instant when its acceleration is 0.5ms^-1.
b) Show that the maximum possible speed of the car is 50ms^-1.

a) using F=ma,
T - R = 1200 * 0.5
T - 400 = 600
T = 1000N

then using P=Tv => v = P/T
v = 20000/1000 = 20m/s

b) speed is greatest when acceleration of the car is 0.
ie: T - R = 1200 *0
T = R = 400N

v = P/T = 20000/400 = 50m/s

Salman

The work done by the car's engine as the car travels from point A to point B is 1500KJ.
c) Given that the car is travelling at its max possible speed between A and B find the time taken to travel from A to B.

c) work done = force * distance
s = 1500000/400 = 3750m

time = distance / speed = 3750/50 = 75s

alternatively, power = work/time
time = work/ power = 1500000/20000 = 75s