Physic - Speed, Velocity and Acceleration

 

Speed

Speed is the distance (D) travelled divided by the time (Δt) taken for the journey.

Quantity: speed (v) 

Unit: metre per second 

Unit symbol: m⋅s−1

Velocity

Velocity is the change in position of a body divided by the time it took for the displacement to occur.

Quantity: average velocity (→v) 

Unit name: metre per second 

Unit symbol: m⋅s−¹

"Distance and time are scalars and therefore speed will also be a scalar."

Example: 

James walks 2km away from home in 30 minutes. He then turns around and walks back home along the same path, also in 30 minutes. Calculate James’ average speed and average velocity.

Step 1: Identify what information is given and what is asked for

The question explicitly gives the distance and time out (2km in 30minutes) the distance and time back (2 km in 30 minutes)

Step 2: Check that all units are SI units.

The information is not in SI units and must therefore be converted.

To convert 

👉Convert (km) to (m), 

we know that, 1km = 1000m

∴2km = 2000m  (multiply both sides by 2)

👉Convert (min) to (sec)

We know that 1mins = 60sec

∴ 30min =1800sec (multiply both sides by 30)

Step 3: Determine James’ displacement and distance.

James started at home and returned home, so his displacement is 0m. 

mΔ= m - m = 0m

James walked a total distance of 4000m (2000m out and 2000m back).

D = 4000m

Step 4: Determine his total time.

James took 1800s to walk out and 1800s to walk back. Δt = 3600s

Step 5: Determine his average speed 

v = d/t 

v = 4000m / 3600s = 1.11m⋅s−¹

Step 6: Determine his average velocity

v = Δx / Δt 

v = 0m / 3600s =0m⋅s−¹

🤔 Differences Between Speed and Velocity

The differences between speed and velocity can be summarised as:

👉 Speed

1. depends on the path taken

2. always positive

3. is a scalar

4. no dependence on direction and so is only positive

👉 Velocity

1. independent of path taken

2. can be positive or negative

3. is a vector

4. direction can be determined from the sign convention used (i.e. positive or negative)

Additionally, an object that makes a round trip, i.e. travels away from its starting point and then returns to the same point has zero velocity but travels at a non-zero speed.

🔸 Acceleration

This is the change in velocity divided by the time taken.

Quantity:  acceleration (→a) 

Unit name: metre per second squared 

Unit symbol: m⋅s−²

Acceleration is a measure of how fast the velocity of an object changes in time. If we have a change in velocity (Δv) over a time interval (Δt), then the  acceleration (a) is given as:

👉  acceleration (in m⋅s−²)

= change in velocity (in m⋅s−²) / change in time (in s)

→a = Δv/t

Acceleration is a vector. Acceleration does not provide any information about the motion, but only about how the motion changes. It is not possible to tell how fast an object is moving or in which direction from the acceleration alone.

Like velocity, acceleration can be negative or positive. We see that when the sign of the acceleration and the velocity are the same, the object is speeding up. If both velocity and acceleration are positive, the object is speeding up in a positive direction. If both velocity and acceleration are negative, the object is speeding up in a negative direction.

"Tip:

Avoid the use of the word deceleration to refer to a negative acceleration. This word usually means slowing down and it is possible for an object to slow down with both a positive and negative acceleration, because the sign of the velocity of the object must also be taken into account to determine whether the body is slowing down or not."

If velocity is positive and acceleration is negative, then the object is slowing down. Similarly, if the velocity is negative and the acceleration is positive the object is slowing down. This is illustrated in the following worked example.

Example:

A car accelerates uniformly from an initial velocity of 2m⋅s-¹ to a final velocity of 10m⋅s−¹ in 8seconds. 

Step 1: Choose a reference frame

We choose the point where the car starts to accelerate as the origin and the direction in which the car is already moving as the positive direction.

Step 2: Identify what information is given and what is asked for

Vi = 2ms−¹ 

Vf = 10m⋅s−¹

(V = 10 - 2 = 8ms-¹)

T = 8s

Step 3: Calculate the acceleration.

a=Δv / Δt

= 8 /  8

=1m⋅s−²

👉Test Questions 👈

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