Acceleration

When we start a car, we observe that it takes time to reach our desired speed.

Now a super car like this, reaches the speed of say 100km/h much faster

Then say, this normal car,

This is because, the engine of the super-car has so much power that, it increases the speed of the car at a faster rate than normal ones.

This rate of change of speed when the direction of motion is taken into account is known as acceleration

Hence, Super-cars can reach their maximum speeds faster than the normal ones

Let’s define acceleration now...

The acceleration is defined generally, as the rate of change of velocity.

Thus, the acceleration a, is defined as $\frac{dv}{dt}$,

Now, if our normal car increases its velocity in a uniform rate, say for every 5 sec, the velocity increases by 15 km/h

Then, the acceleration of our car is said to be constant.

In this case, $a=\frac{dv}{dt}$ becomes, $\text{a dt = dv,}$ upon cross multiplying as a is constant.

Thus we can Integrate RHS from initial to final velocity limits and LHS from initial to final time while keeping $\text{a}$ out of the integrand

Gives, $\text{a t = v - u}$ Thus $a=\frac{v_{final}-u_{initial}}{t}$

$\therefore$, acceleration a, becomes $a=\frac{finalvelocity-initialvelocity}{Timetaken}$

From our definition from Calculus $a=\frac{dv}{dt}$

Lets discuss this further through our super-car

If our super-reaches from 0km/h to 100km/h in just 5 seconds, then acceleration can be calculated

Then, time taken should be written in hours, 60 min * 60 sec = 3600 sec/hr 5 seconds = 5/3600 hours

$$\begin{gathered} So,a=\frac{(100-0)}{5/3600}\frac{km/h}{h} \\ =72000\frac{km}{h^2} \end{gathered}$$

This means, if given an hour time,(and enough fuel), provided the engine can keep accelerating for an hour without blasting!

The super-car can hypothetically reach 72000km/h speed in an hour!!!

But, most super-cars have an upper limit of 300-350km/h so, this speed is not really possible.

Revision

The acceleration a, is defined generally, as the rate of change of velocity.

From Calculus, acceleration becomes $a=\frac{dv}{dt}$ where v is velocity

When velocity changes uniformly in time, the acceleration is constant

When acceleration is constant, $a=\frac{v-u}{t}$ where v and u are final and initial velocites and t is the time taken.

The End