Using the R Position Vector to find Velocity and Acceleration

The video tutorial explains the position equation of an object and derives its velocity and acceleration. It discusses uniformly accelerated motion, highlighting that the highest exponent in the position vector indicates constant acceleration. The tutorial rearranges the position vector to identify it as a uniformly accelerated motion equation, revealing initial conditions. It concludes with an introduction to projectile motion, noting its constant acceleration in the y-direction and constant velocity in the x-direction.

What is the velocity of an object if its position is given by the equation: position equals 2.5 times time in the i direction, plus the quantity 2.5 times time minus 4.9 times time squared in the j direction?

• 2.5 i + (2.5 - 9.8t) j meters per second

• 2.5 i + (2.5 + 9.8t) j meters per second

• 2.5 i + (2.5 - 4.9t) j meters per second

• 2.5 i + (2.5 + 4.9t) j meters per second

What does it mean when an object is in uniformly accelerated motion?

• The acceleration of the object remains constant over time.

• The velocity of the object remains constant over time.

• The acceleration of the object changes over time.

• The velocity of the object changes at a constant rate.

Which of the following is a characteristic of uniformly accelerated motion?

• The highest exponent in the position vector is 1.

• The highest exponent in the position vector is 3.

• The highest exponent in the position vector is 2 or less.

• The position vector has no exponents.

What is the initial velocity of the object in the given position equation?

• 0 i + 2.5 j meters per second

• 2.5 i + 2.5 j meters per second

• 2.5 i + 0 j meters per second

• 0 i + 0 j meters per second

How can you identify that the motion described is projectile motion?

• The object has a constant velocity in both i and j directions.

• The object has an acceleration in the i direction only.

• The object has an acceleration in the j direction and constant velocity in the i direction.

• The object has no acceleration in any direction.