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Using the graph below: What was the instantaneous velocity at t = 12 seconds? What was the distance and displacement of this object between 0 and 15 seconds? What was the average speed and average velocity of this object between 0 and 15 seconds? Finally, what would the velocity-time graph be for this motion?

Using the graph below: What was the instantaneous velocity at t = 12 seconds? What was the distance and displacement of this object between 0 and 15 seconds? Wh class=

Answer :

Answer:

1) 2.5 m/s

2) The distance is 70 m

The displacement is 40 m

3) The average speed is 4.67 m/s

The average velocity is 2.67 m/s

4) The velocity time graph will give the acceleration of the motion

Explanation:

1) The instantaneous velocity is given by the slope at 12 seconds as follows;

Since the distance varies directly with the time from 11 to 15 seconds, the velocity is constant within that time period and is given by the relation;

Velocity = Displacement/(Time duration of displacement)

Velocity = (Final position - Initial position)/(Time duration for the change in position)

Velocity = (-10 - (-20))/(15 - 11) = (-10 + 20)/4 = 10/4 = 2.5 m/s

2) The distance moved by the object between 0 and 15 seconds is given as follows;

Distance = Position 30 to position -25 and from position -25 to position -10

Distance = 30 - (-25) + (-10 - (-25)) = 55 + 15 = 70 m

The displacement = The overall change in position of the object which is the difference between the first and last position;

Displacement = 30 - (-10) = 30 + 10 = 40 m

3) The average speed = Distance/Time = 70/15 = 14/3 = 4.67 m/s

The average velocity = Displacement/Time = 40/15 = 2.67 m/s

4) The velocity time graph will indicate the acceleration of the motion.

As per the graph the instantons velocity at 12 seconds was the distance displacement of the object between the 0 and 15 seconds. The average speed and velocity of time graph be for his motion.

  • At first the instantaneous velocity is given as 12 seconds as follows. Since the distance differs directly with the time of 11 to 15 seconds, the velocity is at the constant within that time.
  • Velocity = Displacement/(Time duration of displacement) . Velocity = (Final position - Initial position)/(Time duration for the change in position) . Hence the Velocity = (-10 - (-20))/(15 - 11) = (-10 + 20)/4 = 10/4 = 2.5 m/s
  • The object between 0 and 15 seconds is given as follows. Distance = Position 30 to position -25 and from position -25 to position -10  Distance = 30 - (-25) + (-10 - (-25)) = 55 + 15 = 70 m
  • The displacement = The overall change in position of the object which is the difference between the first and last position. Displacement = 30 - (-10) = 30 + 10 = 40 m
  • The average speed = Distance/Time = 70/15 = 14/3 = 4.67 m/s . The average velocity = Displacement/Time = 40/15 = 2.67 m/s.
  • Thus the velocity of the time graph will indicate acceleration in the motion.

Learn more about the graph below: What was the instantaneous velocity.

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