Figure depicts the motion of a particle moving along an x axis with a constant acceleration. The figure's vertical scaling is set by xs = 6.0 m. What is the particle's acceleration?
+4 m/
The given graph is a position time graph. This means that at t = 0 the particle is at x = -2
Don't assume the displacement = -2m
That would be wrong.
Since the particle is moving with constant acceleration. That means we can use the equations of motion
Now which one to use
s = ut + 12at2 ∵ we have s— t relation.
Now at t =1 particle has reached x = 0
So the displacement will be 2 m
From x= — 2 to x = 0. Displacement = final position— starting position.
⇒ 2 = u(1) + 12a(1)2
2u + a = 4.............(1)
At t = 2 particle has reached x = 6. So after 2 secfrom start the particle is 8 cm for from starting point.
8=u(2)+12a(2)2
⇒ 2u + 2a = 8
u + a = 4 .... (2)
from equation (1) and (2) we get u + 4 = 4
⇒ u = 0 . ... (3)
Substituting (3) in (2) get a = +4 m/s2
Acceleration =4 m/s2