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    10 Basic Physics Questions: Speed, Force, Acceleration, Velocity.

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    1. A jet flying at 236.9 km/hr travels between two cities in 1.3 hour(s). A turboprop flying the same route takes 5.2 hours. What is the speed of the turboprop?

    2. A 9.0 kg block is free to slide on a frictionless horizontal surface. A force of 4.6 N is applied to the block at an angle of parallel to the horizontal. Find the acceleration of the block (acceleration horizontal only).

    3. A ball thrown straight up with a velocity of 3.0 m/s. How long (seconds) will it take for the ball to reach the highest point?

    4. Initially a woman exerts a constant horizontal force on a large box. As a result, the box moves across a horizontal floor at constant speed "v0". The woman then doubles the constant horizontal force that she exerts on the box to push it on the same horizontal floor. The box then moves:

    5. Two students push a small car down the driveway. The momentum of the 504.7 kg car is plotted as a function of time in the graph above and reaches 3000 kg m/s in 4 seconds. What is the average force of push by each student during the push?

    6. The figure depicts a hockey puck sliding with constant speed v0 in a straight line from point "a" to point "b" on a frictionless horizontal surface. Forces exerted by the air are negligible. You are looking down on the puck. When the puck reaches point "b," it receives a swift horizontal kick in the direction of the heavy print arrow. Had the puck been at rest at point "b,", then the kick would have sent the puck in horizontal motion with a speed vk in the direction of the kick.

    Along the frictionless path taken by the puck after receiving the kick:

    a. is constant for a while and decreases thereafter.
    b. continuously decreases.
    c. continuously increases.
    d. increases for a while and decreases thereafter.
    e. is constant.

    7. A 1353.12 kg car traveling north at 19.84 m/s collides with a 2092.43 kg pickup truck traveling east at 27.04 m/s. The car and pickup truck are locked together at the instant of the collision. What speed do these vehicles go immediately after the collision?

    8. What is the tension on a cable attached to the top of an elevator (with a mass of 1289.2 kg) that is slowing down at 4.54 m/s2 as is travels in the downward direction?

    9. A car accelerates at a constant rate of 5.37 m/s2 from rest at the beginning of a freeway entrance ramp. At the end of the ramp the car has a speed of 26.91 m/s. How long is the ramp?

    10. A lab team acquires data and establishes a mathematical expression that relates circumference to the diameter of circular objects.
    The mathematical model is:
    Circumference = 7.2 (Diameter) + 12.6 cm
    Using the results of this research what would the team estimate the circumference for a circular object with a diameter of 705.7 cm?

    (Please see the attachment for full questions.)

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    SOLUTION This solution is FREE courtesy of BrainMass!

    1.
    The distance between the cities according to the jet is:
    (1.1)
    But according to the turboprop, the distance is:
    (1.2)
    Of course these two distances are the same, so we can equate them and solve for :

    (1.3)
    Plugging in the numbers:

    2.
    A 9.0 kg block is free to slide on a frictionless horizontal surface. A force of 4.6 N is applied to the block at an angle of parallel to the horizontal. Find the acceleration of the block (acceleration horizontal only).
    Newton's second law states that the acceleration vector a of mass M is proportional to the total net force F exerted on it:
    (1.4)
    Since the force is horizontal, the acceleration is horizontal as well/
    Therefore, in our case:


    3.
    A ball thrown straight up with a velocity of 3.0 m/s. How long (seconds) will it take for the ball to reach the highest point?
    The first equation of motion of the ball is that of the instantaneous velocity:
    (1.5)
    Where is the initial velocity of the ball, g is the gravitational acceleration and t is the time elapsed.
    At the maximal height, the instantaneous velocity is zero (otherwise the ball would continue).
    From the velocity equation we get for the time:

    (1.6)
    Plugging in the numbers:


    4.
    Initially a woman exerts a constant horizontal force on a large box. As a result, the box moves across a horizontal floor at constant speed "v0". The woman then doubles the constant horizontal force that she exerts on the box to push it on the same horizontal floor.
    If the box moves with constant velocity, it has no acceleration. Hence, by Newton's second law the net force on the box is zero as well.
    Once the woman doubles the force she exerts on the box, the total net force is no longer zero (assuming other forces such as friction did not change).
    If the total force is not zero then the box accelerates. By the definition of acceleration (the rate of change in the velocity) we see that in this case the velocity will increase continuously.
    The box then moves with continuously increasing speed.

    5.
    Two students push a small car down the driveway. The momentum of the 504.7 kg car is plotted as a function of time in the graph above and reaches 3000 kg m/s in 4 seconds. What is the average force of push by each student during the push?

    The real Newton's second law states that the rate of change in instantaneous momentum equals the instantaneous external force ( is valid only when the mass is constant).
    In other words:
    (1.7)
    In graphical terms, the force is the slope of the momentum-time graph.
    The average force is therefore given by:
    (1.8)
    Where is the total change in the momentum over time interval

    In our case, according to the graph, the change in momentum is and the time interval is so the total average force is:

    Since there are two students involved, the average force exerted by each student is 375N

    6.
    The figure depicts a hockey puck sliding with constant speed v0 in a straight line from point "a" to point "b" on a frictionless horizontal surface. Forces exerted by the air are negligible. You are looking down on the puck. When the puck reaches point "b," it receives a swift horizontal kick in the direction of the heavy print arrow. Had the puck been at rest at point "b,", then the kick would have sent the puck in horizontal motion with a speed vk in the direction of the kick.

    Since after the kick there is no external force acting on the puck, according to Newton's first law it will move with (e) constant speed and in a straight line.

    7.
    Let the north direction be the positive vertical direction while east is the positive horizontal direction
    The car with mass initially moves north with speed
    Therefore its velocity vector is
    (1.9)
    And its momentum vector is:
    (1.10)
    The truck of mass moves due east with speed hence its velocity vector is
    (1.11)
    And its initial momentum is:
    (1.12)
    The system's initial momentum is the vector sum of the truck and car momentums:
    (1.13)
    After the collision, the joined mass is moving with some velocity thus the final momentum is:
    (1.14)

    Since no external forces were involved, the momentum is conserved.
    We equate them and solve for v:

    (1.15)
    The speed after the collision is the magnitude of this vector:

    (1.16)
    Plugging in the numbers:

    Note that since the collision is NOT elastic, kinetic energy is NOT conserved.
    8.
    What is the tension on a cable attached to the top of an elevator (with a mass of 1289.2 kg) that is slowing down at 4.54 m/s2as is travels in the downward direction?

    There are two forces acting on the elevator. One is the tension T, pointing up (and therefore positive) and the second is the elevator's weight Mg, which points down (and therefore negative).
    Thus, the total force on the elevator is
    (1.17)
    The elevator is going down, but the acceleration is in the opposite direction (the elevator slows down), hence the acceleration is positive.
    From Newton's second law we can write:
    (1.18)
    Plugging in the numbers we get for the tension:


    9.
    A car accelerates at a constant rate of 5.37 m/s2 from rest at the beginning of a freeway entrance ramp. At the end of the ramp the car has a speed of 26.91 m/s. How long is the ramp?

    We have already seen that the equation for the instantaneous speed of an object that moves with constant acceleration a is:
    (1.19)
    Integrating this, we get the equation for the instantaneous distance:
    (1.20)
    From equation (1.19):
    (1.21)
    Plugging this in equation (1.20) we get:

    So finaly:
    (1.22)
    We could get to this equation from energy consideartions.
    The force acting on the car is
    (1.23)
    The work done by the force is the force times the distance:
    (1.24)
    The change in kinetic energy is:
    (1.25)
    All the work went to this change in kinetic energy, thus:

    (1.26)
    Plugging the numbers:

    10.
    A lab team acquires data and establishes a mathematical expression that relates circumference to the diameter of circular objects.
    The mathematical model is:
    Circumference = 7.2 (Diameter) + 12.6 cm
    Using the results of this research what would the team estimate the circumference for a circular object with a diameter of 705.7 cm?

    If the diameter is D=705.7 and the circumference in centimeters is given by:
    (1.27)
    Then, plugging in the number into the equation:

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 10:54 pm ad1c9bdddf>
    https://brainmass.com/physics/acceleration/physics-questions-speed-force-acceleration-velocity-518440

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