1

Chapter 6: Motion in a Plane

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Position and Velocity in 2-D

Displacement Velocity Average velocity Instantaneous

velocity Instantaneous

acceleration Average acceleration

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Directions of Instantaneous and average velocities

Instantaneous velocity at any point on the curve is along the tangent drawn at that point

Average velocity points in the direction of the displacement vector

4

Components of velocity

5

Acceleration (Instantaneous and Average)

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Equations of Motion in 2-D

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If a particle’s motion is governed by x=2t2 and y=5t

At any time• What would be its displacement, velocity, and

acceleration?

• What would be its speed?

• What is the angle of inclination?

At t = 5 s• What would be its position, velocity, and acceleration?

• Calculate its speed

• Calculate its angle of inclination θ

8

Projectile Motion

A projectile is an object that moves in 2-D under the influence of only the gravitational force

For projectiles, ax=0 and ay=-g

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Components of velocity and acceleration of a Projectile A projectile is launched

with an initial velocity (9.8,19.6) m/s

Observe that the x-component of velocity is not changing (no change in the length or direction)

Vertical component of the velocity is changing in length and direction due to gravitational force!

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Dynamics of a projectile

Projectile motion is made up of two independent motionsUniform motion with constant velocity along x- direction (horizontal)Free-fall motion in the vertical direction

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Range of a Projectile

Range is the longest horizontal distance traveled by a projectile

What should be θ for the projectile to have longest range?

When would the projectile reach maximum height?

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Projectile Motion as a function of θ