Unit 6 Linear acceleration

What is the difference between average and instantaneous velocity?

Average velocity describes displacement over an interval. Instantaneous velocity describes motion at one moment.

What is displacement?

The signed change in position from start to finish.

When is distance more useful than displacement?

When measuring total ground covered, such as training mileage.

A runner completes one lap. What are distance and displacement?

Distance equals the lap length. Displacement is zero.

What is linear acceleration?

The rate of change of linear velocity.

Is acceleration a scalar or vector?

A vector with magnitude and direction.

What are the SI units of acceleration?

Meters per second squared, m/s².

How do you calculate change in velocity?

Δv = vfinal − vinitial.

How do you calculate average acceleration?

aaverage = (vfinal − vinitial)/Δt.

What determines the direction of average acceleration?

The direction of the change in velocity.

Can an object accelerate without changing speed?

Yes, if its direction changes.

Can an object accelerate without changing direction?

Yes, if its speed changes.

Can acceleration change both speed and direction?

Yes, such as when a skier turns while speeding up.

Does zero acceleration require zero velocity?

No. An object can move with constant velocity.

Does zero velocity at one instant require zero acceleration?

No. An object can momentarily stop while changing direction.

In one dimension, what happens when velocity and acceleration have the same sign?

Speed increases.

In one dimension, what happens when velocity and acceleration have opposite signs?

Speed decreases.

Velocity is positive and acceleration is positive. What happens?

The object speeds up in the positive direction.

Velocity is positive and acceleration is negative. What happens?

The object slows while moving in the positive direction.

Velocity is negative and acceleration is negative. What happens?

The object speeds up in the negative direction.

Velocity is negative and acceleration is positive. What happens?

The object slows while moving in the negative direction.

Does negative acceleration always mean slowing down?

No. It speeds up an object moving in the negative direction.

Does positive acceleration always mean speeding up?

No. It slows an object moving in the negative direction.

For the same velocity change, how does increasing the time affect average acceleration?

It decreases the magnitude of average acceleration.

Why move your hands backward while catching an egg?

It increases stopping time and reduces average acceleration magnitude.

How is average acceleration calculated separately in two dimensions?

ax = Δvx/Δt and ay = Δvy/Δt.

Why should initial and final velocities be compared using components in a 2D problem?

Components preserve directional information.

A basketball player changes forward velocity from 6 to 2.5 m/s in 0.250 s. What is ax?

−14 m/s².

The basketball player changes upward velocity from 0 to 4 m/s in 0.250 s. What is ay?

+16 m/s².

What does the basketball player’s negative horizontal acceleration indicate?

Forward motion is slowing.

What does the slope of a velocity–time graph represent?

Acceleration.

How do you find average acceleration on a velocity–time graph?

Find the slope between two points.

How do you find instantaneous acceleration on a velocity–time graph?

Find the tangent slope at that instant.

What does a horizontal velocity–time line indicate?

Constant velocity and zero acceleration.

What does an upward slope on a velocity–time graph indicate?

Positive acceleration.

What does a downward slope on a velocity–time graph indicate?

Negative acceleration.

What does a steeper velocity–time slope indicate?

Greater acceleration magnitude.

A velocity graph is below zero and slopes upward. Is the object speeding up?

No. Negative velocity and positive acceleration indicate slowing.

At a smooth peak of a velocity–time graph, what is acceleration?

Zero at that instant.

Does the highest velocity on a graph necessarily occur where acceleration is greatest?

No. Greatest acceleration occurs at the steepest upward slope.

How does central difference estimate instantaneous acceleration?

a(t) ≈ [v(t + Δt) − v(t − Δt)]/(2Δt).

Velocity is 2 m/s at 0.9 s and 4 m/s at 1.1 s. Estimate acceleration at 1.0 s.

10 m/s².

What does acceleration perpendicular to velocity change instantaneously?

The direction of motion.

What defines a propulsive phase?

Speed increases because velocity and acceleration point in the same direction.

What defines a braking phase?

Speed decreases because velocity and acceleration point in opposite directions.

What does this deck call a phase with constant velocity and zero acceleration?

A static phase, which can include steady motion.

On a position–time graph, what does slope represent?

Velocity.

A bar-height graph rises and becomes steeper. What is the bar doing?

Moving upward and speeding up.

A bar-height graph rises but flattens. What is the bar doing?

Moving upward and slowing down.

A bar-height graph falls and becomes steeper downward. What is the bar doing?

Moving downward and speeding up.

A bar-height graph falls but flattens. What is the bar doing?

Moving downward and slowing down.

When can the constant-acceleration equations be used?

When acceleration stays constant over the interval.

Which equation finds final velocity using initial velocity, acceleration, and time?

vfinal = vinitial + aΔt.

Which equation finds displacement using initial velocity, acceleration, and time?

d = vinitialΔt + ½a(Δt)².

Which constant-acceleration equation does not require time?

vfinal² = vinitial² + 2ad.

In the constant-acceleration equations, does d mean distance or displacement?

Signed displacement.

A puck starts at 30 m/s and stops over 25 m with constant acceleration. What is its acceleration?

−18 m/s².

How long does that puck take to stop?

Approximately 1.67 seconds.

A cyclist moves downhill and brakes. Which direction must acceleration point to slow her?

Opposite her downhill velocity.

Does having good acceleration mean having the highest top speed?

No. Acceleration describes changes in velocity, while top speed describes maximum speed.