Linear motion
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LINEAR MOTION. TICKER TAPE.

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LINEAR MOTION

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Linear motion

LINEAR MOTION


Ticker tape

TICKER TAPE

A ticker-timer consists of an electrical vibrator which vibrates 50 times per second. This enables it to make 50 dots per second on a ticker-tape being pulled through it. The time interval between two adjacent dots on the ticker-tape is called one tick. One tick is equal to 1/50 s or 0.02 s.


Uniform velocity

UNIFORM VELOCITY

  • The distance of the dots is equally distributed.

  • All lengths of tape in the chart are of equal length.

  • The object is moving at a uniform velocity.


Uniform acceleration

UNIFORM ACCELERATION

  • The distance between the dots increases uniformly.

  • The length of the strips of tape in the chart increase uniformly.

  • The velocity of the object is increasing uniformly, i.e. the object is moving at a constant acceleration.


Uniform deceleration

UNIFORM DECELERATION

  • The distance between the dots decreases uniformly.

  • The length of the strips of tape in the chart decreases uniformly.

  • The velocity of the object is decreasing uniformly, i.e. the object is decelerating uniformly.


Example 1

EXAMPLE 1

Diagram 2.4 shows a strip of ticker tape that was pulled through a ticker tape timer that vibrated at 50 times a second. What is thea. time taken from the first dot to the last dot?b. average velocity of the object that is represented by the ticker tape?


Answer

ANSWER

  • a. There are 15 ticks from the first dot to the last dot, henceTime taken = 15 × 0.02s = 0.3sb. Distance travelled = 15cm

    v=s/t

    v=15cm/0.3s

    v=50cms-1


Example 2

EXAMPLE 2

The ticker-tape in figure above was produced by a toy car moving down a tilted runway. If the ticker-tape timer produced 50 dots per second, find the acceleration of the toy car.


Answer1

ANSWER


Example 3

EXAMPLE 3

A trolley is pushed up a slope. Diagram above shows ticker tape chart that show the movement of the trolley. Every section of the tape contains 5 ticks. If the ticker-tape timer produced 50 dots per second, determine the acceleration of the trolley.


Answer2

ANSWER


Equation of linear motion

EQUATION OF LINEAR MOTION


Example 11

EXAMPLE 1

  • A car is approaching a stoplight moving with a velocity of +30.0 m/s. The light turns yellow, and the driver applies the brakes and skids to a stop. If the car acceleration is -8.00 m/s2, then determine the displacement of the car during the skidding process.


Answer3

ANSWER

  • Given:

    vi = +30.0 m/s vf = 0 m/s

    a = - 8.00 m/s2

  • (0 m/s)2 = (30.0 m/s)2 + 2(-8.00 m/s2)s

    0 m2/s2 = 900 m2/s2 + (-16.0 m/s2)s

    (16.0 m/s2)s = 900 m2/s2 - 0 m2/s2

    (16.0 m/s2)s = 900 m2/s2

    s = (900 m2/s2)/ (16.0 m/s2)

    s = (900 m2/s2)/ (16.0 m/s2)

    s = 56.3 m


Example 21

EXAMPLE 2

  • A bus is waiting at a stoplight. When it finally turns green, the bus accelerated from rest at a rate of a 6.00 m/s2 for a time of 4.10 seconds. Determine displacement of the bus during this time period.


Answer4

ANSWER

  • Given:

    vi = 0 m/s t = 4.10 s

    a = 6.00 m/s2

  • s = (0 m/s)(4.1 s) + 0.5(6.00 m/s2)*(4.10 s)2

    s = (0 m) + 0.5(6.00 m/s2)(16.81 s2)

    s = 0 m + 50.43 m

    s = 50.4 m


Problem 1

PROBLEM 1

  • An airplane accelerates down a run-way at 3.20 m/s2 for 32.8 s until is finally lifts off the ground. Determine the distance traveled before take-off.


Answer5

ANSWER

  • d = vi*t + 0.5*a*t2

  • d = (0 m/s)*(32.8 s)+ 0.5*(3.20 m/s2)*(32.8 s)2

  • d = 1720 m


Problem 2

PROBLEM 2

  • A car starts from rest and accelerates uniformly over a time of 5.21 seconds for a distance of 110 m. Determine the acceleration of the car.


Answer6

ANSWER

  • d = vi*t + 0.5*a*t2

  • 110 m = (0 m/s)*(5.21 s)+ 0.5*(a)*(5.21 s)2

    110 m = (13.57 s2)*a

    a = (110 m)/(13.57 s2)

    a = 8.10 m/ s2


Problem 3

PROBLEM 3

  • It was once recorded that a Jaguar left skid marks which were 290 m in length. Assuming that the Jaguar skidded to a stop with a constant acceleration of -3.90 m/s2, determine the speed of the Jaguar before it began to skid.


Answer7

ANSWER

  • vf2 = vi2 + 2*a*d

  • (0 m/s)2 = vi2 + 2*(-3.90 m/s2)*(290 m)

    0 m2/s2 = vi2 - 2262 m2/s2

    2262 m2/s2 = vi2

    vi = 47.6 m /s


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