Question

Which of the following sentences contains an example of instantaneous velocity?
A. The car covered 500 kilometres in the first 10 hours of its northward journey.
B. Five seconds into the launch, the rocket was shooting upwards at 5000 metres per second.
C. The cheetah can run at 70 miles per hour.
D. Moving at five kilometres per hour, it will take us eight hours to get to the base camp.
E. Roger Bannister was the first person to run one mile in less than four minutes.

Answer 1

Hint: Try to think of what instantaneous velocity means, if velocity is the rate of change of position of an object with respect to time in a particular direction. In other words, instantaneous velocity specifies the speed and direction of an object at a particular instant of time. Use this definition as a checklist to narrow down on the options.

Complete answer:
Let us begin by establishing an understanding of instantaneous velocity.
We know that velocity is a specification of an object’s speed and direction, and speed is the distance travelled by an object in a given time.
Now, instantaneous velocity specifies an object’s speed and direction (velocity) at a particular time or an instant. In the same way, instant speed specifies an object’s speed at a particular time or an instant.
Additionally, we have something called the average speed and average velocity. Suppose we have an object that executes a non-uniform motion, where it takes different amounts of time to cover the same distances over a path. This means that the object covers different distances of the path at different speeds. In such a case the average speed gives the mean speed of the object. If this speed is specified with a direction, it is called as average velocity.
Now, let us look at the options given to us and deduce which of the definitions we’ve established fit.
As for option A: We have a distance and a direction and we have information over a time of 10 hours. So, this will be an average velocity.
Option B: We have a distance and direction at a particular instance of time. So, this will be an instantaneous velocity.
Option C: We have the maximum speed a cheetah can reach, which means that at some instant the cheetah reaches the speed specified. So this is an instantaneous speed.
Option D and E specify only the speed and a calculative deduction. So these two are cases of average speed.

Therefore, the option that specifies an instantaneous velocity is: B. Five seconds into the launch, the rocket was shooting upwards at 5000 metres per second.

Note:
Do not forget that the instantaneous velocity is the specific rate of change of position with respect to time at a single point in time which we call an instant, and the average velocity is the average rate of change of position with respect to time over a time interval. The same applied for speed, except speed does not entail any directional information.