Question

A body covers a distance 20 m in 7th second and 24 m in 9th second. if the motion is uniformly accelerated, then find the value of acceleration

Answer 1

Answer:

Assuming the body is under uniform acceleration, let the velocity at 7th and 9th second be v7 and v9. Thus the body will travel 36m in the 15th second.

Explanation:

This implies Uniform acceleration = (24–20)/2

Thus acceleration a=2 m/s2

Now, distance travelled in 15th second is Veloctiy at t=15 s. Let's call it V15;

According the well known formula:

V15= U7 + a*time = 20+(2*8) = 36 m/s

Thus the body will travel 36m in the 15th second.

Answer 2

Given: A body covers 20 m in 7th second and 24 m in 9th second.

To find: Value of acceleration

Explanation: Distance travelled in 7th second= 20 m

Distance travelled in 9th second= 24 m

Formula for calculating distance travelled in nth second is given by:

S = u + a(2n-1)/2

In first case, n= 7 and S= 20 m

20= u+ a(2*7-1)/2

=> 20 = u+ 13a/2

=> 40= 2u+13a....(i)

In second case, n=9 and S= 24 m

24= u+a(2*9-1)/2

=> 24= u+ 17a/2

=> 48= 2u+17a...(ii)

Subtracting (i) from (ii),

8 = 4a

=> a = 8/4

= 2 m/s^2

Therefore, the value of acceleration is 2 m/s^2.