Question

A helicopter’s speed increases from 25 m/s to 60 m/s in 5 seconds. What is the acceleration of this helicopter?

Answer 1

ANSWER :-

♦ Some terms :-

→ Initial Speed :- The speed at which the object moves during start of measurement of motion.

→ Final Speed :- The speed at which the object moves at the end of the measurement of motion.

→ Acceleration :- It is the rate of Change of velocity .

♦ As given :-

→ Initial Speed :- 25 m/s

→ Final Speed :- 60 m/s

→ Time :- 5 sec

♦ Now by using motion equation ..

v = u + at

>> By substituting values

→ 60 = 25 + 5a

→ 60 - 25 = 5a

→ 35 = 5a

→ a = 35 ÷ 5

→ a = 7

♦ So acceleration = 7 m/s²

Answer 2

Here, two different speeds are given, one is intial speed and other is final speed.

Before reckoning acceleration, let's understand what this terms actually mean.

$\boxed{\bold{\mathsf{Initial\:speed:}}}$

The speed which is at starting of any object is called as initial speed.

$\boxed{\bold{\mathsf{Final\:speed:}}}$

The speed which is at ending of any object is called as final speed.

The initial speed and the final speed always differ because we know that, when objects starts they gain very little amount of speed to start, further they go on increasing it. When the object has to stop, they completely decrease their speed.

$\boxed{\bold{\mathsf{Acceleration:}}}$

Acceleration is rate of change of velocity.

Now we know, what this terms actually mean. Now, we can reckon the acceleration of the helicopter as asked in the above question.

Given that,

Initial speed = 25 m/s

Final speed = 60 m/s

Time = 5 s

Before reckoning further, we've to always check that, everything is given in its SI unit or not.

Here, everything is given in its SI unit. So, we can compute the acceleration.

If not, convert the given units into their SI units.

By using first equation of motion,

v = u + at

60 = 25 + a(5)

60 - 25 = 5a

35 = 5a

$\frac{35}{5}$ = a

$\frac{\cancel{35}}{\cancel{5}}$ = a

7 m/s = a

$\boxed{\bold{\mathsf{acceleration = 7\:m/s^2}}}$

Therefore, the acceleration of the helicopter is 7 m/s².

We can also calculate it by using another formula.

Alternative method:

Acceleration = $\frac{v - u}{t}$

Acceleration = $\frac{60 - 25}{5}$

Acceleration = $\frac{35}{5}$

Acceleration = $\frac{\cancel{35}}{\cancel{5}}$

$\boxed{\bold{\mathsf{Acceleration = 7\:m/s^2}}}$

Therefore, the acceleration of the helicopter is 7 m/s².

$\pink{\boxed{\bold{\mathsf{Note:}}}}$

We can't directly cancel out 60 and 5 or - 25 and 5 as they are different terms. If there was a multiplication or division sign, we can cancel out it.

As we know that, only plus (+) and minus (-) signs segregate the terms and not multiplication (×) and division (÷) signs.