Acceleration and Velocity

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What did Galileo conclude about the rate of change of velocity with time for objects in free fall?

Galileo concluded that the rate of change of velocity with time is a constant of motion for all objects in free fall.

How is instantaneous acceleration defined?

Instantaneous acceleration is defined as the slope of the tangent to the v-t curve at a specific instant.

What does the acceleration-time curve represent?

The acceleration-time curve represents how acceleration changes over time.

When is acceleration considered uniform?

Acceleration is considered uniform when it has a constant value over a specific time interval. Signup and view all the answers

What is the relationship between average acceleration and uniform acceleration?

When acceleration is uniform, it equals the average acceleration over that period. Signup and view all the answers

What did Galileo find about the change in velocity with distance for objects in free fall?

Galileo found that the change in velocity with distance is not constant; it decreases with increasing distance of fall. Signup and view all the answers

Explain the relationship between velocity and acceleration.

Velocity is a quantity with both magnitude and direction, while acceleration can result from a change in speed, a change in direction, or changes in both. Signup and view all the answers

Describe the position-time graphs for motion with positive, negative, and zero acceleration.

The graph curves upward for positive acceleration, downward for negative acceleration, and is a straight line for zero acceleration. Signup and view all the answers

What does it mean for acceleration to be constant?

Acceleration is constant when its value remains the same during the motion interval. Signup and view all the answers

If the velocity of an object is $v_0$ at $t=0$ and $v$ at time $t$, what is the equation relating velocity, initial velocity, acceleration, and time?

The equation is $v=v_0 + a(t-0)$ or $a = rac{v-v_0}{t-0}$. Signup and view all the answers

Give an example of an object moving in the positive direction with a negative acceleration.

An example is the motion of the car in Fig 3.3 between $t=18s$ and $t=20s$. Signup and view all the answers

Provide an example of an object moving in the negative direction with a negative acceleration.

An example is the motion of a car moving from O in Fig. 3.1 in the negative x-direction with increasing speed. Signup and view all the answers

Define instantaneous acceleration.

Instantaneous acceleration is defined as the limit of the average acceleration as the time interval approaches zero. Signup and view all the answers

How is acceleration related to the slope of the velocity-time graph?

The acceleration of an object at a particular time is the slope of the velocity-time graph at that instant of time. Signup and view all the answers

What is the significance of the area under the velocity-time curve?

The area under the velocity-time curve between times t1 and t2 is equal to the displacement of the object during that interval of time. Signup and view all the answers

Explain the relationship between displacement, time, initial velocity, final velocity, and acceleration in uniformly accelerated rectilinear motion.

In uniformly accelerated rectilinear motion, displacement x, time taken t, initial velocity v0, final velocity v, and acceleration a are related by kinematic equations: v = v0 + at, x = v0t + 1/2at^2, v^2 = 2v0^2 + 2ax. Signup and view all the answers

What is the difference between path length and displacement?

The displacement depends only on the end points, while the path length depends on the actual path taken. Signup and view all the answers

Describe the x-t and v-t graphs for uniform motion and motion with uniform acceleration.

For uniform motion, x-t graph is a straight line inclined to the time axis, and the v-t graph is a straight line parallel to the time axis. For motion with uniform acceleration, x-t graph is a parabola, and the v-t graph is a straight line inclined to the time axis. Signup and view all the answers