Concept of Acceleration Units, Definitions & Examples:

Overview:

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