Question

A body moving with a constant acceleration
travels the distances 3 m and 8 m respectively in 1
s and 2 s. Calculate : (i) the initial velocity, and (ii)
the acceleration of body.

Ans. (i) 2 m/s, (ii) 2 m/s²​

Answer 1

Answer:

Initial velocity is 2 m/s and acceleration of body is 2 $m/s^2$

Step-by-step explanation:

Equation of motion is

$s = ut + \frac{1}{2}at^2$

where, u = Initial Speed, t = Time, a = acceleration

Now, given that a body travels 3 m in 1 s

Thus, substituting the values in equation of motion, we get

$3 = u(\,1)\, \frac{1}{2}a(\,1)\,^2\\\\ 3 = u + \frac{a}{2}\\\\ 6 = 2u + a\\\\ a + 2u = 6 ------ (1)$

Now, also given that a body travels 8 m in 2 s

Thus, substituting the values in equation of motion, we get

$8 = u(\,2)\, \frac{1}{2}a(\,2)\,^2\\\\ 8 = 2u + \frac{a}{2} \times 4\\\\ 8 = 2u + 2a\\\\ a + u = 4 ------ (2)$

Solving Eq(1) and (2), we get

   a + 2u = 6

   a + u = 4

  (-)   (-)    (-)

-----------------------

      u = 2

Putting u = 2 in (2), we get

$a + 2 = 4\\\\ a = 4 - 2\\\\ a = 2$

Thus, we get

$Intial\hspace{0.1cm}Velocity = 2m/s$

$Acceleration = 2m/s^2$

Answer 2

Answer:

Ans. (ii) 2 m/s²

Step-by-step explanation:

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