Question

Which of the following graphs gives the equation \[x = {v_0} + \dfrac{1}{2}a{t^2}\]
A.
B.
C.
D. None of these

Answer 1

Hint:The second equation of motion gives the total distance covered by an object which is moving with uniform acceleration. To solve this question, we need to define the velocity-time graphs using the variation of velocity. To draw a v-t graph, the area under it is defined as the distance.

Complete step by step solution:
A velocity-time graph represents the variation of velocity of a moving particle with respect to the time taken. For the accelerated motion, the line will not be parallel to the x-axis as well as the y-axis. For another graph that is with zero acceleration, the line will be parallel to the X axis or we can say that time axis.

This graph represents a velocity-time graph for the accelerated motion.

This represents the velocity-time graph for the accelerated motion and for the motion for zero acceleration.

Now look at this graph,

As we know that the distance covered by a body is equal to the enclosed area under that graph,

Hence option C is the correct answer

Note: A velocity-time graph or v-t graph shows the speed as well as the direction an object travels over a specific period of time. Velocity-time graphs are also known as speed-time graphs. The y-axis or vertical axis of a velocity-time graph is the velocity of the object and the x-axis or horizontal axis of a velocity-time graph is the time of the object.