At t = 0 seconds, a cart is moving with a velocity of 10 cm/s and an acceleration of 4.0 (cm/s)/s. assuming its acceleration stays at this value, what will its velocity be 7.0 seconds later?

For this case what you should do is write the kinematic equations to find the final speed.
 We have then:
 a = a
 vf = a * t + vo
 Where,
 vf: final speed
 a: acceleration
 t: time
 vo: initial speed.
 Substituting the values we have:
 vf = (4.0) * (7.0) + (10)
 vf = 38 cm / s
 
 its velocity will be 38 cm / s 7.0 seconds later

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