# Concept of Acceleration Units, Definitions & Examples:

#### Overview:

 Topic Included: Formulas, Definitions & Exmaples. Main Topic: Quantitative Aptitude. Quantitative Aptitude Sub-topic: Time Speed and Distance Aptitude Notes & Questions. Questions for practice: 10 Questions & Answers with Solutions.

#### Concept of Acceleration:

Rate of change of velocity of any moving object is known as Acceleration.

#### Concept of Acceleration Formula:

$$\left[a = \frac{V_f - V_i}{T}\right]$$

Where,
$$a$$ = Acceleration.
$$T$$ = Time taken
$$V_f$$ = Final velocity of moving object.
$$V_i$$ = Initial velocity of moving object.

#### Concept of Acceleration Examples:

Example (1): If the initial speed of a car is $$20 \ m/sec$$ and speed increases to $$50 \ m/sec$$, within $$10 \ seconds$$, then find out the acceleration of the car?

Solution: Given values,
initial speed of the car $$(V_i) = 20 \ m/sec$$

final speed of the car $$(V_f) = 50 \ m/sec$$

Time taken $$(T) = 10 \ seconds$$, then $$\left[Acceleration \ (a) = \frac{V_f - V_i}{T}\right]$$ $$\left[Acceleration \ (a) = \frac{50 - 20}{10}\right]$$ $$Acceleration \ (a) = \frac{30}{10} = 3 \ m/sec^2$$

Example (2): If the initial speed of a bus is $$x \ m/sec$$ and due to acceleration of $$20 \ m/sec^2$$ the speed of bus increases to $$1500 \ m/sec$$, within $$60 \ seconds$$, find out the value of $$x$$ ?

Solution: Given values,
initial speed of the car $$(V_i) = x \ m/sec$$

final speed of the car $$(V_f) = 1500 \ m/sec$$

Time taken $$(T) = 60 \ seconds$$,

acceleration $$(a) = 20 \ m/sec^2$$ then $$\left[Acceleration \ (a) = \frac{V_f - V_i}{T}\right]$$ $$\left[20 = \frac{1500 - x}{60}\right]$$ $$x = 300 \ m/sec$$

Example (3): If the initial speed of a bicycle is $$200 \ m/sec$$ and due to acceleration of $$5 \ m/sec^2$$ the speed of bus increases to $$y \ m/sec$$, within $$15 \ seconds$$, find out the value of $$y$$ ?

Solution: Given values,
initial speed of the car $$(V_i) = 200 \ m/sec$$

final speed of the car $$(V_f) = y \ m/sec$$

Time taken $$(T) = 15 \ seconds$$,

acceleration $$(a) = 5 \ m/sec^2$$ then $$\left[Acceleration \ (a) = \frac{V_f - V_i}{T}\right]$$ $$\left[5 = \frac{y - 200}{15}\right]$$ $$y = 275 \ m/sec$$

Example (4): If the initial speed of a vehicle is $$350 \ m/sec$$ and due to acceleration of $$8 \ m/sec^2$$ the speed of bus increases to $$550 \ m/sec$$, within $$t \ seconds$$, find out the value of $$t$$ ?

Solution: Given values,
initial speed of the car $$(V_i) = 350 \ m/sec$$

final speed of the car $$(V_f) = 550 \ m/sec$$

Time taken $$(T) = t \ seconds$$,

acceleration $$(a) = 8 \ m/sec^2$$ then $$\left[Acceleration \ (a) = \frac{V_f - V_i}{T}\right]$$ $$\left[8 = \frac{550 - 350}{t}\right]$$ $$t = 25 \ sec$$