Question

What will be the slope of the velocity time graph?
A. acceleration
B. velocity
C. displacement
D. None of these

Answer 1

We should use the basic definition for the acceleration in order to solve this question. The acceleration can be found by taking the rate of variation of the velocity of a body with respect to the time taken. This is a vector quantity which is having both magnitude and direction. This will help you in answering this question.

Complete answer:
The acceleration can be found by taking the rate of variation of the velocity of a body with respect to the time taken. This is a vector quantity which is having both magnitude and direction. When a body is moving from one point to another in a particular time, its velocity will change. Because a body is going from one point to another and the change in velocity does not remain constant. Therefore the slope of the velocity time curve will be equal to the tangent of the angle between the curve and time axis. This will be equivalent to the first derivative of the velocity.
$\tan \theta =\dfrac{dv}{dt}$
Where $\theta$ be the angle between the curve and the time axis. Therefore the slope of a velocity time graph will be the acceleration. This has been mentioned as option A.

So, the correct answer is “Option A”.

Note: The slope of the line on a velocity time graph reveals useful information about the acceleration of the body. When the acceleration is zero, then the slope will tend to be zero. That means the horizontal line. If the acceleration is found to be positive, the slope will also be positive. That means in the upward sloping line also remember that the area under the velocity time graph gives the distance covered by the object.