Lesson test: Describing motion

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Describing motion

1.[1p]
What does the slope of a chord on a graph of position against time represent?

The average velocity between the two endpoints of the chord

Correct

The instantaneous velocity at the midpoint

The answer is: The average velocity between the two endpoints of the chord

The acceleration over that interval

The answer is: The average velocity between the two endpoints of the chord

The distance travelled over that interval

The answer is: The average velocity between the two endpoints of the chord

2.[2p]
A negative acceleration always means the body is slowing down.

True

The answer is: False

False

Correct

3.[2p]
A trolley moves with $x (t) = 12 t - 1.5 t^{2}$ metres. What is its velocity, in metres per second, at $t = 3$ s?

CorrectNot quite: 3

4.[2p]
A car brakes from 25 m s⁻¹ at a steady 6.25 m s⁻². How many metres does it travel before stopping?

CorrectNot quite: 50

5.[2p]
A stone is dropped from rest. Taking $g = 9.81$ m s⁻², how far has it fallen after 2.5 s, in metres?

CorrectNot quite: 30.7

6.[3p]
Why do the equations of motion need exactly two initial conditions?

Because acceleration is the second derivative of position, so recovering position takes two integrations, each with one constant

Correct

Because motion happens in two dimensions

The answer is: Because acceleration is the second derivative of position, so recovering position takes two integrations, each with one constant

Because both distance and displacement must be specified

The answer is: Because acceleration is the second derivative of position, so recovering position takes two integrations, each with one constant

Because velocity and speed are different quantities

The answer is: Because acceleration is the second derivative of position, so recovering position takes two integrations, each with one constant

7.[3p]
Which of these statements about a body thrown vertically upward are correct, ignoring air resistance?

Select all that apply

Its speed is zero at the highest point

Correct

Its acceleration is $g$ downward throughout, including at the highest point

Correct

Its velocity changes sign at the highest point

Correct

Its acceleration is zero at the highest point

The answer is: Its speed is zero at the highest point, Its acceleration is $g$ downward throughout, including at the highest point, Its velocity changes sign at the highest point

8.[2p]
Match each quantity to what it is the derivative of, with respect to time.

Velocity
Acceleration
Speed

velocity
distance travelled
position

Show the answer

Velocity: position Acceleration: velocity Speed: distance travelled

9.[2p]
A car drives forward, then brakes to rest, then reverses. Put these values of the pair (velocity, acceleration) in the order they occur.

Negative velocity, negative acceleration
Positive velocity, zero acceleration
Positive velocity, negative acceleration
Zero velocity, negative acceleration

Show the answer

a, b, c, d

1.[1p] What does the slope of a chord on a graph of position against time represent?

2.[2p] A negative acceleration always means the body is slowing down.

3.[2p] A trolley moves with x(t)=12t−1.5t2 metres. What is its velocity, in metres per second, at t=3 s?

4.[2p] A car brakes from 25 m s⁻¹ at a steady 6.25 m s⁻². How many metres does it travel before stopping?

5.[2p] A stone is dropped from rest. Taking g=9.81 m s⁻², how far has it fallen after 2.5 s, in metres?

6.[3p] Why do the equations of motion need exactly two initial conditions?

7.[3p] Which of these statements about a body thrown vertically upward are correct, ignoring air resistance?

8.[2p] Match each quantity to what it is the derivative of, with respect to time.

9.[2p] A car drives forward, then brakes to rest, then reverses. Put these values of the pair (velocity, acceleration) in the order they occur.

1.[1p]
What does the slope of a chord on a graph of position against time represent?

2.[2p]
A negative acceleration always means the body is slowing down.

3.[2p]
A trolley moves with $x (t) = 12 t - 1.5 t^{2}$ metres. What is its velocity, in metres per second, at $t = 3$ s?

4.[2p]
A car brakes from 25 m s⁻¹ at a steady 6.25 m s⁻². How many metres does it travel before stopping?

5.[2p]
A stone is dropped from rest. Taking $g = 9.81$ m s⁻², how far has it fallen after 2.5 s, in metres?

6.[3p]
Why do the equations of motion need exactly two initial conditions?

7.[3p]
Which of these statements about a body thrown vertically upward are correct, ignoring air resistance?

8.[2p]
Match each quantity to what it is the derivative of, with respect to time.

9.[2p]
A car drives forward, then brakes to rest, then reverses. Put these values of the pair (velocity, acceleration) in the order they occur.