Question

A truck covers \[2000km\] in \[18hrs\] next \[700km\] in \[7hrs\] and \[1100km\] in \[9hrs\]. Calculate average speed and average velocity of the truck.

Answer 1

Hint: Scalar quantity has magnitude but no direction while vector quantity has both magnitude and direction. First of all identify the scalar and vector quantity in the given question and then find the total distance and displacement of the moving body. It will help you to find out the right solution.

Complete step by step answer:
According to the question,
Total covered distance by the truck will be
 = \[2000km + 700km + 1100km\]
= \[3800km\]
Total displacement of the truck will be
= \[2000km - 700km - 1100km\]
= \[200km\]
Total time elapsed by the truck is
= \[18hrs + 7hrs + 9hrs\]
=\[34hrs\]
Now,
We know that,
The average speed can be measured by using the formula
= \[\dfrac{{Dis\tan ce}}{{Time}}\]
\[\dfrac{{3800}}{{34}} = 111.76km/hr\]
The average velocity can be measured by using the formula
= \[\dfrac{{Displacement}}{{Time}}\]
\[\dfrac{{200}}{{34}} = 5.88km/hr\]
Average Speed- Average speed can be defined as the total distance covered by the object in total time. It is a scalar quantity and its SI unit is m/s.
Average Velocity- The average velocity is the ratio of total displacement of the object to the total time taken. Displacement is either smaller than or equal to the distance. This is the reason , the magnitude of average velocity is either less than or equal to the average speed.

Note:
The magnitude of displacement and the total path length covered of the object is always the same. When the object is moving along the straight line, then in this condition the magnitude of the average velocity is always equal to the average speed. But when the object is moving in different directions then in this case average speed is not equal to the magnitude of the average velocity. Here path length is greater than the magnitude of displacement.