What is Average Velocity?
The change in displacement (∆x) or location divided by the time intervals (∆t) in which the displacement happens is termed the average velocity. Average velocity is a vector quantity depending upon the sign of the displacement; the average velocity can be positive or negative. Metres per second (m/s or ms-1) is the SI unit of average velocity.
Average velocity can also be defined as the occurrence of displacement of any particular object in a specific period with respect to the original position. Besides this, the ratio of total displacement to total time taken for any particular object is also known as average velocity.
The formula for average velocity is,
V = D/t
Where,
Average velocity = V
Total displacement = D
Total time taken is = T
which turns the formula into,
Average Velocity = displacement/time
The direction of average velocity is the same its displacement direction. However, if an object contains a changeable speed that changes its magnitude frequently, its direction would remain the same as the direction of displacement. It can be noticed that the magnitude of average velocity is nearly the same or a bit less than that of the average speed. This is because displacement can be noticed as either equal or a little less than the total distance to be covered.
Finding Average Velocity
We need to divide the total displacement by the total time elapsed to calculate the average velocity, which is:
v =Δx/Δt = xf−x0/tf−t0
Where, ΔV = average velocity,
Δx = displacement
Δt = total time, xf and x0 are the initial and final positions, the initial and final times are tf and t0
If the initial time is zero, then the formula becomes
v =Δx/t
Difference between Average Velocity and Average Speed
Only the displacement of the object is involved in Average velocity, though the magnitude of the displacement may be dissimilar from the actual path length. Therefore, we use average speed to describe the rate of motion over a path.
Whereas the total length of the path travelled divided by the total time interval of the motion is known as average speed. Average speed is always positive because it does not tell us the direction of motion. The average speed is a scalar quantity, and the average velocity is a vector quantity.
Important Questions on Average Velocity
1) What does the velocity v/s time graph of a ball falling from a height before hitting the ground?
a) A straight line with a positive slope
b) A parabola
c) A hyperbola
d) A straight line with a negative slope
Correct Option: (a)
Explanation: As the ball falls, its velocity increases because of the acceleration due to gravity. Therefore, the graph looks like a straight line with a positive slope. The first equation of motion can vary this.
2) What is the correct formula for average velocity?
a) v = x/t
b) v = dx/dt
c) v = xt/x
d) v = xt
Correct Option: (a)
Explanation: The average velocity is the total change in displacement divided by the total change in time. Therefore, v = dx/dt is the formula for instantaneous velocity.
3) To complete a journey of 200 km, a truck requires 4 hrs, calculate the average speed.
a) 50 km/hr
b) 30 km/hr
c) 20 km/hr
d) 5 km/hr
Correct Option: (a)
Explanation: The average speed is the total distance divided by total time taken. The total distance is 200 km, and the total time taken is 4 hrs; therefore, the average speed = 200/4 = 50 km/hr.
4) Between points A and B, the average speed of a car is 30 m/s, between B and C is 20 m/s, and between C and D is 15 m/s. Calculate the average speed between A and D, if the time taken in the stated sections is the 20s, 10s and 5s, respectively?
a) 25 m/s
b) 10 m/s
c) 15 m/s
d) 30 m/s
Correct Option: (a)
Explanation: Since, the average speed is the total distance divided by the total time taken, the total displacement (d = vt) = 30×20 + 20×10 + 15×5 = 875 m. Total time = 20 + 10 + 5 = 35 s. Therefore, average speed = 875/35 = 25 m/s.
5) Which of the following statements is correct?
a) Average speed > Instantaneous speed
b) Average speed >= Instantaneous speed
c) Average speed <= Instantaneous speed
d) Average speed < Instantaneous speed
Correct Option: (c)
Explanation: The ratio of the total distance to total time is average speed, and the ratio of the instantaneous change in distance to instantaneous change in time is instantaneous speed. Therefore, the average speed can be equivalent to instantaneous speed, which is generally less than that.
6) The speed varies from 0 to 30 m/s in 5 s. Find the average speed during the motion.
a) 10 m/s
b) 20 m/s
c) 0 m/s
d) 15 m/s
Correct Option: (d)
Explanation: According to the first equation of motion, v = u + at,
where v= 30m/s u = 0 m/s and t = 5 s which means that a = 6 m/s2.
Now, from the second equation of motion s = ut + (1/2) at2, where u = 0m/s, a= 6 m/s2 and t = 5 s, which means that s = 75 m.
Therefore, average speed = s/t = 75/5 = 15 m/s.
7) When a body falls under gravity with terminal velocity, what will happen to its average velocity?
a) Average velocity increases
b) Average velocity decreases
c) Average velocity remains constant
d) Average velocity changes exponentially
Correct Option: (c)
Explanation: The velocity does not change when the body moves with terminal velocity. This means that in equal intervals of time. Therefore, the average velocity remains constant.
8) What can be said about the average velocity thrown up in the sky and falling back after reaching a certain height?
a) The average velocity is non zero
b) The average velocity is zero
c) The average velocity is greater than zero
d) The average velocity is less than zero
Correct Option: (b)
Explanation: The positive displacement is covered by the ball when it goes up and the negative displacement when it comes down, which means that the total displacement is zero. Hence, the average velocity is zero.
9) What can be said about the average velocity of a car moving in a circular path around a pole?
a) The average velocity is non zero
b) The average velocity is zero
c) The average velocity is greater than zero
d) The average velocity is less than zero
Correct Option: (b)
Explanation: The car is moving in a circle, and hence, after a definite time interval, it will come back to the same point. Therefore, the average velocity is zero because the displacement is 0.
10) Find the average velocity when the changes in displacement in three consecutive instances are 8 m, 10 m, 12 m, and the total time taken is 6 s.
a) 5
b) 3
c) 4
d) 9
Correct Option: (a)
Explanation: The total change in displacement = 30 m that is, (8+10+12). Now, the total time is taken = 6 s. Therefore, the Average velocity = total change in displacement/total time taken = 30/6 = 5 m/s.
Practice Questions
1) Define average velocity.
2) Define average speed.
3) When is the average velocity zero?
4) Is average velocity a scalar or a vector quantity?
5) Define acceleration.
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