A body is at rest at . At , it starts moving in the positive -direction with a constant acceleration. At the same instant another body passes through moving in the positive -direction with a constant speed. The position of the first body is given by after time ‘’ and that of the second body by after the same time interval. Which of the following graphs correctly describes as a function of time ‘’

General solution of  is

In the following graph, distance travelled by the body in metres is

Velocity-time graph for a moving object is shown in the figure. Total displacement of the object during the time interval when there is non-zero acceleration and retardation is

The value of k such that lies in the plane 2x-4y+z+7=0 is

So here we used the concept of three dimensional geometry to understand and solve the question. Any point's position or coordinates in 3D space are determined by how far they have travelled along the x, y, and z axes, respectively. So here the value of k is 7.

The distance between the line and the plane is (units)

The number of solutions of the equation  where  for  in the interval   is

The displacement-time graph of a moving object is shown in figure. Which of the velocity-time graphs shown in figure could represent the motion of the same body?

The value of k for which the lines and are perpendicular is

If the straight lines x=1+s,y=-3-λs,z=1+λs and , z=2-t, with parameters s and t respectively, are co planar, then λ=

If 5 cas 

A boy begins to walk eastward along a street infront of his house and the graph of his displacement from home is shown in the following figure. His average speed for in the whole-time interval is equal to

The values of  satisfying  and  are

A body of mass is resting on a wedge of angle as shown in figure. The wedge is given at acceleration . What is the value of a son that the mass just falls freely?

A cyclist starts from the centre of a circular park of radius one kilometre, reaches the edge of the park, then cycles along the circumference and returns to the centre along as shown in figure. If the round trip takes ten minutes, the net displacement and average speed of the cyclist (in metre and kilometre per hour) is

A ball is thrown vertically upwards. Which of the following graph/graphs represent velocity-time graph of the ball during its flight (air resistance is neglected)