This is a presentation on the graph of the nature of motion of objects. It is useful for A level physics

A football is dropped from the top of a tall building. Which acceleration-time graph best represents the motion of the football through the air?

As the football is dropped from the height in presence of air(air resistance is taken into account) displacement of the football goes on decreasing and attains terminal velocity. As the displacement decreases acceleration also decreases and finally becomes zero. Hence Graph C illustrates the behavior. In graph C acceleration goes on decreasing and attains zero acceleration finally.

Which displacement-time graph best represents the motion of a falling sphere, the initial acceleration of which eventually reduces until it begins to travel at constant terminal velocity?

For terminal velocity , corresponding displacement is a straight line. Graph D illustrates the nature .

When a car driver sees a hazard ahead, she applies the brakes as soon as she can and brings the car to rest. The graph shows how the speed v of the car varies with time t after she sees the hazard

Here v is constant in the beginning so corresponding displacement is a straight line which is illustrated in B,C and D.As seen later, velocity is a straight line ,corresponding displacement can’t be a straight line as illustrated in B, also it can’t be increasing and decreasing as in graph D. Now graph C shows the straight line displacement initially, and displacement decreasing further. Hence graph C illustrates the nature of the motion.

We know as the ball falls freely under gravity from height h, displacement of the ball goes on increasing as time passes ( neglecting air resistance) by the formula s=1/2at^2. The height decreases at higher rate as time passes which is illustrated by graph B. Graph B illustrates the height decreasing at higher rate as time passes. So graph B is the answer.

This question is a tricky question. Here it says it is falling in air but freely means the force acting on the object is just because of its weight that is it has constant acceleration due to gravity . (Here is no air resistance) Also we know the object falls faster as time passes by. That means the distance goes on increasing as time passes by which is illustrated by graph A.

In a projectile motion, the force on an object is only due to force of gravity. We know in a projectile motion velocity is constant in horizontal direction this implies net force is zero in horizontal direction. Only the force exerted on the object is in the vertical direction because of force of gravity . So forces acting is along XV only. So the answer is A.

As the ball falls vertically under gravity without air resistance it falls faster as time passes by which is shown by Graph A.

As time passes by sphere moves slower because of viscous force(opposing force) and finally attains a constant velocity(terminal velocity) hence Graph D illustrates the nature of the motion.

The force due to air resistance is zero when she leaves the balloon . As she falls down, the force due to gravity increases until she reaches the terminal velocity after which constant force is applied . Hence graph B illustrates the nature of the motion.

As shown in the second figure, though the current is zero the pointer reads the current to be X. Hence the calculation has positive zero. It overestimates the value compared to the true value. The measured value made by the instrument has to be subtracted .Hence as it overestimates the reading graph A is the correct answer.

When speed increases uniformly with time then speed time graph is a straight line. This implies acceleration is constant hence graph A is the correct answer.

Here velocity time graph is increasing uniformly upward upto 1st marking hence displacement goes on increasing upward .Again velocity time graph is a constant hence displacement is a straight line upto 2nd marking. Velocity decreases with time hence displacement also decreases as illustrated in graph C between 2nd and 3rd marking.

We know in projectile motion the only force acting is in vertical direction because of force due to gravity. Here the skier velocity decreases reaching upto the peak and then increases as it falls down which is clearly illustrated by graph D.

Here as you see the signal repeats after every 5 squares. One square has a time base setting 2.00ms hence 5 squares means 10.0 ms . This implies the time period(T) of the signal is 10.0 ms. The frequency f=1/T=100Hz Hence the answer is B.

Velocity 0 means rest hence the jumper is at rest at point R . At point Q , the velocity is constant hence acceleration is zero. Hence the nature of motion of jumper is depicted by option C.

Velocity is increasing as time passes hence displacement also has to increase, decreases in the positive y-axis hence hence displacement also has to decrease as time passes by, velocity becomes zero hence displacement is constant or stationary(slope of S-t has to be zero , further velocity increases in the negative y direction hence displacement has to increase downward, finally velocity decreases hence displacement has to decrease . This nature is very much explained by graph A.