**Acceleration** of an object is the rate of change of velocity with respect to time.

- SI unit is metre per second square or metre per second per second ($m \, s^{-2}$)
- Vector quantity
- $ a = \frac{v – u}{t}$, where v is final velocity, u is initial velocity and t is time taken.
- If the velocity of an object
**increases**, the object is undergoing**acceleration**. Hence, if the velocity of an object**decreases**, it is undergoing**deceleration**. - If the velocity of the object is
**constant**, the acceleration is**zero**. - An object is said to be undergoing uniform acceleration when there is a constant change in velocity per unit time.

**Note:** If the direction of an object changes, it is undergoing acceleration by definition. Change direction = change in velocity = acceleration (Might not be that important in O level)

### Worked Examples

**A bus starts from rest and achieves a velocity of $20 \text{ m s}^{-1}$ in 10 seconds while moving to the right. Calculate its average acceleration.**

### Show/Hide Answer

Average acceleration:

$$\begin{aligned} \left< a \right> &= \frac{v-u}{t} \\ &= \frac{20-0}{10} \\ &= 2 \text{ m s}^{-2} \text{ towards the right} \end{aligned}$$

**A car travelling westwards at $30 \text{ m s}^{-1}$ suddenly comes to a halt in 5 s. Find its average acceleration.**

### Show/Hide Answer

$$\begin{aligned} \left< a \right> &= \frac{v-u}{t} \\ &= \frac{0-30}{5} \\ &=-6 \text{ m s}^{-2} \text{ towards the west} \end{aligned}$$

Note that $-6 \text{ m s}^{-2} \text{ towards the west}$ is the same as $6 \text{ m s}^{-2} \text{ towards the east}$.

Neglecting air resistance, ALL objects experiences the same gravitational acceleration of 10 $m \, s^{-2}$ towards the centre of the Earth (commonly referred to as “downwards” in questions).

- Note:
**Constant**acceleration of $10 \, \text{m s}^{-2}$ - The above means that the speed of a
**downward-falling**object (neglecting air resistance and other forces that is not gravity) will experience an**increase**of $10 \, \text{m s}^{-1}$ every second. - It also means that the speed of an object
**travelling upwards**(neglect the same forces as above) will experience a**decrease**of $10 \, \text{m s}^{-1}$ every second. - In general, the faster the object travel, the greater the air resistance.
- When an object falls (without neglecting air resistance), it experiences acceleration and an increase in velocity. This will cause air resistance acting on the object to increase as well. There will be a point where the air resistance is large enough to balance the gravitational force. This will cause the resultant force to be 0, and there will be 0 acceleration. The object will reach constant velocity, which is termed as terminal velocity.

The magnitude of gravitational acceleration of the Earth is determined by the mass of the Earth, and not by the mass of the object. This means that a feather and a bowling ball will fall at the SAME rate if you neglect air resistance.

Check out the video below: (Skip to 1.25 min mark for the “with air resistance” part and 2.50 min mark for the “absence of air resistance” (vacuum) part.)

**Important kinematics equation! (Memorize them!)**

$v = u + at$

$s = ut + \frac{1}{2} at^{2}$

$v^{2} = u^{2} + 2as$

$s = \frac{1}{2} (u + v) t$

,Where

v = final velocity

u = initial velocity

a = acceleration

t = change in time

s = change in displacement

**NOTE:** These equations are ONLY valid IF AND ONLY IF acceleration is **constant**. (Very Important!)

### Self-Test Questions

**Would you consider a car turning around a corner at a constant speed to be accelerating?**

### Show/Hide Answer

Yes! Acceleration is defined as the rate of change of velocity.

Velocity has two components – magnitude and direction.

When the car is turning around a corner, it’s direction is constantly changing.

Since the direction is constantly changing, the velocity will be constantly changing. (i.e. The car is accelerating!)

**Does motion always take place in the direction of acceleration?**

### Show/Hide Answer

No! Consider a car that is moving towards the right at a velocity of $25 \text{ m s}^{-1}$. If the driver steps on the brakes and slowly brings the car to a stop, the direction of the acceleration will be towards the LEFT during the whole deceleration process. (Even though the car is still moving towards the left!)

**Can an object be moving if its acceleration is zero?**

### Show/Hide Answer

Yes! An object that maintains a constant velocity (that is above/below $0 \text{ m s}^{-1}$) will be moving with a zero acceleration.

**A stone is thrown upwards into the air. Assuming negligible air resistance, what is the magnitude and direction of its acceleration?**

### Show/Hide Answer

The magnitude of its acceleration is $10 \text{ m s}^{-1}$ and the direction is downwards.

Salim scribbled

hello

i would like to understand something.

if, according to Einstein, the ball and the feathers are not moving, why did the box and the falling objects come into contact at the end of the experiment?

I would greatly appreciate an answer but ONLY if you are 100% sure about it.

thanks.

Salim scribbled

hello

Since I have not received any reply I will try to answer my question myself 🙂

It has to do with the theory of relativity.

We saw the feather and the ball fall because of our standpoint; we were watching them from outside the chamber.

But what if we were standing on the feathers themselves, would we see the feathers as moving? No. The feathers would seem still even though they would be falling. Same as we seem to be standing still on Earth despite the fact that the Earth is moving.

If you do not agree, please let me know your views.

mitq55 scribbled

you are right according to Einstein

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