Question

The position (x) of a particle moving along x-axis varies with time (t) as shown in figure. The average acceleration of particle in time interval t = 0 to t= 8s is...,

1) 3 m/s^2
2) -5 m/s^2
3) -4 m/s^2
4) 2.5 m/s^2

Answer 1

The answer to this question is option 2.

slope it tan(theta) of the x-t curve gives us the velocity
therefore find the slope at t=0 gives vel v1 and slope at t=8 gives final velocity v2 

now it is equal to V2-V1/t2-t1
and also v2 is -ve because slope at t=8 is-ve
therefore v2=-20 and v1 =20 put values 
in formula, we get a= -5 

Slope of x-t 

velocity at t = 0 is given by  slope tan Θ
tan Θ = P/B = 40/2 = 20 = V₁

the slope at t = 8

tan Θ = -40/2 = -20 = V₂

V₂ is negative as Q > 90°

acceleration = V₂-V₁/ t₂-t₁ = -20-20/8-0 = -40/8

= -5 m/s²