Question

A body initially at rest travels a distance of 100m in 5s with constant acceleration. calculate the acceleration and velocity at the end of 5s​

Answer 1

GIVEN :

• Distance, S = 100 m.
• Time taken, t = 5 sec.

TO CALCULATE :

• The acceleration and velocity at the end of 5 sec.

FORMULAS USED :

• $\sf S \: = \: ut \: \dfrac {1}{2} \: at^{2}$
• $\sf V \: = \: u \: + \: at$

SOLUTION :

To find the acceleration = ?

$\sf Using \: S \: = \: ut \: + \: \dfrac {1}{2} \: at^{2}$

$\implies \sf 100 \: = \: 0 \: + \: \dfrac {1}{2} \: \times a \: \times \: 5^{2}$

$\implies \sf 100 \: = \: \dfrac {1}{2} \: \times \: a \: \times 25$

$\implies \sf 100 \: = \: \dfrac {25}{2} \: a$

$\implies \sf a \: = \: \dfrac {100}{4} \: \times \dfrac {2}{25}$

$\implies \sf a \: = \: \cancel{100} \: \times \: \dfrac{2}{\cancel{25}}$

$\implies \sf 4 \: \times \: 2$

$\large\red {\boxed {\sf a \: = \: 8 \: m/s^{2}}}$

Now, to find the velocity = ?

$\sf Using \: V \: = \: u \: + \: at$

$\sf V \: = \: 0 \: + \: 8 \: \times \: 5$

$\large\red {\boxed {\sf V \: = \: 40 \: m/s}}$