Multiple Choice Questions (MCQs): Graphical Representation of Motion - JEE MCQ

Because velocity is the slope of the x-t graph.(dx/dt=V) and by looking at the graph it can be seen that upto time T₀ slope is constant so velocity will be constant and after time T0 slope is zero ( line is parallel to X axis) so the velocity will be zero.

Calculate the area of the graph as area of v-t grph gives dis. 1/2×4×15=30

We have given in the information that the person is in his office for two hours hence his position must not vary for two hours, that is the horizontal part in the graph which is only observed in the graph of option c.

From the given graph we get that the area of the given graph is total distance covered that is 
=  ½ x 10 x 12
=  60m
And total time taken is 10 sec
Thus average speed is  60m / 10sec
 = 6 m/s

This can be verified graphically

ObtaIning instantaneous acceleration from graph

Velocity is a physical vector quantity; both magnitude and direction are needed to define it. The scalar absolute value (magnitude) of velocity is called "speed", being a coherent derived unit whose quantity is measured in the SI (metric system) as metres per second (m/s) or as the SI base unit of (m⋅s⁻¹).

Given:

Let two balls A and B have mass m_A, m_B respectively, and their initial velocities are u_A and u_B. After the collision, they will move with the same velocity, v_o. 

Given that mass of both balls are same.

So  m_A = m_B = m

u_A = V,  u_B = 0

From the Concept of Momentum Conservation:

m_Au_A + m_Bu_B = (m+m)v_o

mV = 2mv_o

v_o = V/2

Both the balls after impact will move with velocity v/2.

A velocity time graph represents the velocity of an object at a very certain time. If two curves collide that means that their velocities at the given time are equal. Their acceleration may or may not be equal depending upon the slope of the curve at the point of intersection.

Correct option is C. Not possible to extend the graph to second quadrant as time cannot be negative.

The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality. The boundary line is dashed for > and < and solid for ≤ and ≥.