When a clock reads 5.0 seconds a cart's velocity in the negative x direction is 3.0 m/s. when the clock reads 6.0 seconds, the cart's velocity in the positive x direction is 4.0 m/s. what is the magnitude (in m/s2) of the average acceleration of the cart?

Impulse is the change of momentum before and after the collision:
I = mv₁ - mv₂ = m (v₁-v₂)
m mass
v velocity

Impuls also is defined as the average force during a short period of time:
I = F * t = m * a * t
F average force
t time difference
m mass
a average acceleration

Combined:
m(v₁- v₂) = m * a * t
a = (v₁- v₂) / t
= (4m/s - (-3m/s)) / 6s - 5s
= 7m/s / 1s
= 7 m/s²

9.375m/s

Explanation: This is an inelastic collision, so the formula is mv1+mv2=(m1+m2)v-final. My work is a follows:

2500kg(12m/s) + 700kg(0m/s)=(2500kg+700kg)(v-final)

30,000kg(m/s)+0=3200kg(v-final)

30,000kg(m/s)/3200kg=9.375m/s