Question

(a) Derive the formula s = ut + 1/2 at2, where the symbols have usual meanings.

Answer 1

Answer:

s = ut + 1/2 at 2

Explanation:

Let us consider an object moving along a straight line with uniform acceleration a . Let at an instant t ds be the infinitesimally small displacement of the object in infinitesimally small time interval dt. Then its instantaneous velocity v is given by

Answer 2

Explanation:

• Let us consider a body moving in a linear motion with an initial velocity, u.
• The body is moving in a uniform acceleration and achieves a final velocity, v after a certain time, t. The straight line AB is the velocity-time graph as shown below.

Now, from the below figure,

Initial velocity,  $u=o$

A at $t=0$

Final velocity, $v=O C$ at $t=t$

So, the distance travelled, s in time, t= area of the trapezium OABD.

$s=\frac{1}{2} \times(O A+D B) \times O D$

$=\frac{1}{2} \times(u+v) \times t$

As we know, $v=u+a t,$

So, $s=\frac{1}{2} \times(u+u+a t) \times t$

$=\frac{1}{2} \times(2 u+a t) \times t$

$=\frac{1}{2} \times(2 u t+a t 2)$

$=\frac{1}{2} \times 2 u t+\frac{1}{2} a t 2$

$=\frac{1}{2} \times 2 u t+\frac{1}{2} a t 2$

Therefore, $s=u t+\frac{1}{2} a t 2$.