[Physics] Differentiate b/w scalar and vector in Newtonian mechanics

accelerationkinematicsnewtonian-mechanicsvectorsvelocity

I am reading the definitions of vector and scalar quantities.

Scalar quantity – quantity with magnitude only.

Vector – quantity with magnitude and direction.

After that we have some quantities to distinguish,

But i am confuse with some quantities

  1. Why speed is scalar and acceleration is vector? I think both include movement.

  2. Why force vector it has no direction i guess.

  3. What is the difference between velocity and speed? Because one is vector other scalar.

Please explain in layman language.

Edit –

Let i want to explain this to someone who dont have knowledge of formulas.

Best Answer

Your definitions of scalars and vectors are fine.

In specific answer to your questions:

  1. and 3, are related, so I'll address them first:

$$\text{speed} = \frac{\text{distance}}{\text{time}}$$

and

$$\text{velocity} = \frac{\text{displacement}}{\text{time}}$$

Where distance is

a scalar quantity that refers to "how much ground an object has covered" during its motion.

displacement is

a vector quantity that refers to "how far out of place an object is"; it is the object's overall change in position.

$$\text{displacement} = \text{change in position} = \text{final position} - \text{initial position}$$

The direction is based on where the final position is with respect to the initial position.

(time is also a scalar)

(Reference for quotes about distance and displacement).

Due to velocity being calculated based on the vector displacement, velocity is also a vector (going in the same direction as the displacement). Similarly, acceleration is based on a change in velocity, so is a vector as velocity is a vector.

$$\text{acceleration} = \frac{\text{change in velocity}}{\text{time}}$$

in the direction of the velocity - if the acceleration is negative, the object is decelerating (slowing down) or accelerating in the opposite direction.

Similarly for question 2. Force is calculated using the vector acceleration:

$$\text{force} = \text{mass} \cdot \text{acceleration}$$

in the direction of the acceleration.

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