Question

A car moving with uniform acceleration travels 80 m in the first 6 s and 160 m in the next 5 s. Find the initial velocity and acceleration of the body.​

Answer 1

Part - 1 :

• Distance travelled by the car = 80 m

• time taken by the car = 6 s

By using the 2 nd kinematic equation ,

$s = ut + \frac{a {t}^{2} }{2}$

here ,

• s = distance
• u = initial velocity
• a = acceleration
• t = time

$80= 6 u+ \frac{a \times {6}^{2} }{2}$

$80= 6u + 18a...(1)$

For finding the final velocity use the I st kinematic equation

$v = u + at$

$v = u + 6a$

Part - II :

• Distance travelled by the car = 160m

• time taken by the car = 5 s

• The final velocity of part I will become the initial velocity of part II

u ' = v = u + 6 a

$160= 5u ' + \frac{a \times {5}^{2} }{2}$

$160 = 5(u + 6a)+ 12.5a$

$160 = 5u + 42.5a...(2)$

Now multiplying (1) by 5 we get ,

$400= 30u + 90a...(3)$

Now multiplying (2) by 6 we get ,

$960= 30u + 255a...(4)$

Subtracting (3) from (4) we get ,

$360 = 165a$

$\boxed{a = 2.2 \frac{m}{ {s}^{2} }}$

Substituting the value of a in eq ( 1)

$80= 6u + 18 \times 2.2$

$6u = 80 - 39.6$

$u = \frac{40.4}{6}$

$\boxed{u = 6.7 \frac{m}{s}}$