Question

If a body travels with uniform acceleration 5 ms for 5 sec and with uniform acceleration 10 m/s² for next 10 sec then its average acceleration in m/s² is?

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Answer 1

Information provided with us :

• If a body travels with uniform acceleration 5 ms for 5 seconds
• That same body travels with uniform acceleration 10 m/s² for next 10 seconds

What we have to calculate :

• Average acceleration in m/s²

Using Formulas :

First equation of motion :-

• v = u + at

Here,

• v is is final velocity,
• u is initial velocity,
• a is acceleration
• t is time taken

Performing Calculations :

$\red\bigstar$ Finding out final velocity after 5 seconds:-

• We know that initial velocity is always zero when an body is started moving, in the question it is given that uniform acceleration is 5m/s² so it would be the acceleration, and time taken is 5s.

We have :

• a is 5m/s
• t is 5s
• u is 0
• v = ?

Putting the values in first equation of motion :

$: \longmapsto \: \sf{v \: = \: 0 \: + \: (5)(5)}$

$: \longmapsto \: \sf{v \: = \: 0 \: + \: (5) \times (5)}$

$: \longmapsto \: \sf{v \: = \: 0 \: + \: 5 \times 5}$

$: \longmapsto \: \sf{v \: = \: 0 \: + \: 25}$

$: \longmapsto \: \red{\boxed{\sf{v \: = \: 25ms {}^{ - 1} }}}$

$\therefore \underline{\bf{ Final \: velocity \: after \: 5 \: seconds \: is \: 25ms {}^{ - 1} }}$

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$\red\bigstar$Finding out final velocity for next 10 seconds:-

• We know that now intial velocity will be 25 m/s , in the question it is clearly mentioned that acceleration is 10m/s² and time taken is 10s

We have :

• u is 25 m/s
• t is 10s
• a is 10 m/s²
• v = ?

Putting the values in first equation of motion :

$: \longmapsto \: \sf{v \: = \:25 \: + \: (10)(10)}$

$: \longmapsto \: \sf{v \: = \:25 \: + \: (10) \times (10)}$

$: \longmapsto \: \sf{v \: = \:25 \: + \: 10 \times 10}$

$: \longmapsto \: \sf{v \: = \:25 \: + \: 100}$

$: \longmapsto \: \red{\boxed{\sf{v \: = \: 125ms {}^{ - 1} }}}$

$\therefore \underline{\bf{ Final \: velocity \: for \: next \: 10 \: seconds \: is \: 125ms {}^{ - 1} }}$

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$\red\bigstar$Finding out average acceleration:-

We know that average acceleration is calculated by,

• $\green{\underline{\boxed{\tt{Acceleration \: = \: \dfrac{Change \:in \: velocity}{total \: time} }}}}$

We have :

• Total time = 10 + 5 = 15s
• Change in velocity = $\sf{v_2 \:- \: v_1}$
• Change in velocity = 125 - 25 = 100

Putting the required values :

$: \implies \: \sf{Average \: acceleration \: = \: \dfrac{100}{15} }$

$: \implies \: \sf{Average \: acceleration \: = \: \cancel\dfrac{100}{15} }$

$: \implies \: \sf{Average \: acceleration \: = \: \dfrac{25}{3} }$

$\underline{\bf{Henceforth , average \: acceleration \: in \: m/s {}^{2} \: is \: 25/3 \: m/s {}^{2} }}$

Answer 2

Given :

• If a body travels with uniform acceleration 5 ms for 5 sec and with uniform acceleration 10 m/s² for next 10 seconds

To Find :

• Average acceleration in next 10s

Solution :

Using first equation of motion we get :

=> 0 + 25

=> 25

Again using first equation of motion :

=> 25 + 100

=> 125

Now, average acceleration would be :

=> Average acceleration = 100 / 15

(Remember that 15 is total time)

=> Average acceleration = 25/3

Hope it helps ! $\:$