Question

Area under speed-time graph is equal to the:
A) Velocity of the body
B) Magnitude of the displacement
C) Distance travelled by the body
D) None of these

Answer 1

Recall that speed is defined as the rate at which the object covers a particular distance in a particular time. It has only magnitude and no direction. So, it is a scalar quantity. The object that is not moving at all has no speed. Distance of a body is indicated by using an arrow. It is denoted by using the symbol ‘d’.

Complete step by step answer:
Step I:
Speed of a body is measured as the ratio of distance to the time taken by the object to cover the distance. Mathematically, it is written as
$Speed = \dfrac{{Dis\tan ce}}{{Time}}$
Or $Dis\tan ce = Speed \times Time$
Distance of a body depends on the path taken by the body and it can change according to the path.

Step II:
In order to calculate the distance covered by an object or the speed of the object, graphs can be used. The speed-time graph is used to understand the distance travelled by the object.

Step III:
$\Rightarrow$ Option C is the right answer.

Note: It is important to note that the term distance and displacement are not the same. They are both different and not to be confused. Distance is a scalar quantity and displacement is a vector quantity. Displacement is the length of the minimum path between two points and distance is the complete length. Distance can be measured along a straight or curved path but displacement can only be measured along a straight path. The distance of a body can have only positive values but displacement can have positive, negative and zero values.