Question

A body moves along a straight line with acceleration 3 ms-2 for 2 seconds and then with acceleration
4 ms-2 for 3 seconds. What is its average acceleration?
(A) 3.4 ms-2
(B) 3.5 ms-2
(C) 3.6 ms-2
(D) 3.7 ms-2​

Answer 1

A body moves along a straight line with acceleration 3 m/s² for 2 sec.

Here..

Acceleration of body (a1) = 3 m/s²

Time (t2) = 2 sec

Later the body moves with acceleration 4 m/s² for 3 sec.

Here...

Acceleration (a2) = 4m/s²

Time (t2) = 3 sec

According to question,

We have to find the average acceleration of the body.

Now,

Total time = t1 + t2

→ 2 + 3

→ 5 sec

Average acceleration = Acceleration of body in first case + Acceleration of body in second case

Let average acceleration be "a".

→ at = a1t1 + a2t2

Substitute the known values in above formula

→ a(5) = 3(2) + 4(3)

→ 5a = 6 + 12

→ 5a = 18

→ a = 18/5

→ a = 3.6 m/s²

∴ Average Acceleration is 3.6 m/s².

Option B) 3.6 m/s²

Answer 2

$\huge{\underline{\underline{.........Answer.........}}}$

$\huge{\underline{Given:-}}$

Body moves with acceleration of 3m/ s² for 2 seconds.

and,Body moves with acceleration of 4m/s² for 3 seconds.

t¹ = 2 seconds.

t²= 3 seconds.

$\huge{\underline{Explanation:-}}$

Total time = 2 + 3 = 5 seconds.

From the average acceleration formula.

Let the acceleration be a'.

a't = at¹ + a"t².

a'(5) = 3 × 2 + 4 × 3

$a' = \frac{6 + 12}{5}$

$a' = \frac{18}{5}$

$a' = 3.6$

$\boxed{\boxed{a' = 3.6 m/s^2}}$

So, average acceleration of body is 3.6 m/s².