Test: Motion in a Straight Line (Graphs) - JEE MCQ

Until and unless the velocity of any object comes to zero, any peek in its displacement-time graph can’t be achieved. Which means for the height to be maximised the velocity must become zero. And any time of this motion the acceleration is always a constant downward due to gravity.

When an object is thrown from a height a continuous gravitational acceleration acts upon the body and hence time of flight can written equal to√2gs when we consider initial velocity to be zero. Now as we can see even if initial velocity is not zero, time of flight does not depend upon the mass of the body. Hence the time of flight is always the same ideally.

Uniform force acting = 3i + j N
Displacement done = (4-2)i + 3j + (-1-1)k
= 2i + 3j -2k
Thus total work done = F.s (dot product here)
We get W = 3 x 2 + 1 x 3 + 0 x -2
= 9J

Angular velocity is defined as the rate of change of angular displacement with respect to time. It is usually expressed by a Greek letter ω (omega).
Mathematically, angular velocity,
ω =dθ/dt
If a body is rotating at the rate of N r.p.m. (revolutions per minute), then its angular velocity,
ω = 2πΝ / 60 rad/s

Because if acceleration is not constant then it becomes non intertial frame. Thus this equations are only use when acceleration is constant intertial frame

The child should hold the umbrella in the direction at which the rain appears to fall on him, which is the direction of relative speed of rain with respect to the  child.

1. Linear momentum is not constant but angular momentum is
2. Speed has to be constant for “uniform” circular motion
3. For obvious reasons ω is constant
4. And the same goes for α

If we write the equation of motion for both the masses and derive a simple equation to find the maximum vertical height let say H, we get for any particle for some mass m,
H = v² / 2a
Where a is gravitational acceleration and v is vertical speed. Thus as H does not depend upon m, we get both particles would have equal maximum height.

A freely falling body observes a constant downwards force of gravity which hence applies a constant downward acceleration upon the body.

We know that velocity is the first derivative of change in displacement wrt time, hence we get 
V = 3at²