Question

an object is accelerated uniformly,it's displacement after 2s is given 18m and 4s is given 52 m.calculate
a) acceleration
b) initial velocity
c) displacement after 10s​

Answer 1

Explanation:

Let initial velocity = u

Let uniform acc. = a

After 2s

t1 = 2s

displacement, s1 = 18m

using 2nd eqn of motion

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

18 = 2u + 1/2 × a × 4

18 = 2u + 2a

9 = u + a__________________i

After 4s

t2 = 4s

displacement, s2 = 56m

Using 2nd eqn of motion

56 = 4u + 1/2 × a × 16

56 = 4u + 8a

14 = u + 2a________________ii

Solving eqn i and hi

subtract i from ii

a = 5m/s^2

putting value of a in eq 1

u = 4m/s

Displacement after 10s

t = 10s

using 2nd eq of motion

s = 4×10 + 1/2×5×10×10

s = 40 + 250

s = 290m