Olimpiade Sains Pra-OSK Fisika

A billiard ball initially has an initial speed v0, then is accelerated with an acceleration value that is in the direction of speed and is proportional to its speed with the equation: a=kv a=dv/dt. With k as a constant and v is the speed. Determine the position equation as a function of time t if the initial position of the billiard ball x0=0!

• x=v0k(e^(kt)-1)

• x=v0k(e^(3kt)-1)

• x=2v0k(e^(3kt)-3)

• x=2v0k(e^(kt)-3)

• x=v0k(e^(3kt))

Two objects of the same mass are moving and have velocity vectors u=4v i + v j + 3 k and w=v i - 6x j + 5 k. For both vectors to be perpendicular and collide only once, what is the value of v?

• x=24/3

• x=20/3

• x=-6

• x=-7

• x=-24/3

The result of measuring heat that...

Determine the units of α and β in the equation Q̇(t) = αT + βt, where Q̇(t) represents the heat passing through a pipe over a certain time (in J/s), t in seconds, and T in degrees Celsius.

• kgm²/s³ and kgm²/s³

• kgm²/s⁴ and kgm²/s³

• kgm²/s³ and kgm²/s⁴

• kgm²/s³ °C and kgm²/s⁴

• kgm²/s⁴ °C and kgm²/s³

A mass m is rotated using a string on a table with constant speed and radius. The gravitational acceleration experienced by the object is constant g. The force felt by the ball is given by F = C v^x r^y m^z, where C is a constant. Determine the value of x + y - z!

• 0

• 1

• 2

• 3

• 4

A car is accelerated with a constant acceleration α from rest for a certain time and then decelerated with a constant deceleration β until it stops. If the total time of acceleration and deceleration is t seconds, what is the maximum speed of the car?

• v_max = 3αβt / (α + β)

• v_max = 2αβt / (α + β)

• v_max = αβt / (α + β)

• v_max = 3αβt / (α - β)

• v_max = 2αβt / (α - β)

A stone is dropped from a height h=100 m. After 4 seconds, a second stone is thrown upwards from the ground with a speed v_0=50 m/s. When do the two stones meet in the air?

After 4 seconds, the second stone is thrown upwards from the ground with a speed of v0=50 m/s. When the two stones meet in the air, determine the time t1 after the first stone is dropped.

• t1=5 s

• t1=3.5 s

• t1=2 s

• t1=1.5 s

• t1=1 s

Two balls move as shown in the image. One ball descends from the peak of a smooth triangle and the other ball moves along a parabolic trajectory at an elevation angle φ. Both balls reach point P at the same time and speed. Determine the angle of projection of the ball φ!

• cosα=0.635

• cosα=0.735

• cosα=0.835

• cosα=0.935

• cosα=1.035

A circle is on a smooth horizontal floor. On the circle, there is a particle moving without friction as shown in the image, the initial position of the particle is exactly in the center of the circle. Determine the speed when the particle is about to leave the circle!

• v = √(2gR/3)

• v = √(gr)

• v = √(4gR/3)

• v = √(3gR/2)

• v = √(5gR/2)