Many students think that an object's acceleration is always in the direction in which the object is moving
Misconception
Some studies have found that students commonly think that the direction of an object's acceleration will always be in the same direction as that object's velocity. Students may, for instance, struggle to grasp that a car coming to a stop at a red light will have an acceleration that is opposite in direction to its velocity.
Resources to Address This

Acceleration and Deceleration
Source  SPT Mo03PN06
This resources introduces the idea of acceleration in directions that oppose velocity.
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Acceleration Changes Velocity
Source  SPTFm02PN02
This resource helps explain the relationship between velocity and acceleration more clearly for students.
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Nonuniform acceleration with a tickertimer
Source  Practical physics / Force and Motion / Acceleration /....
The experiment shows that acceleration is not always constant. In fact acceleration can change and itself have a rate of change. The rate of change of distance (or, more strictly, 'displacement') is called velocity. The rate of change of velocity is called acceleration. The rate of change of acceleration has no name so it's hard to get hold of the concept.
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References
The following studies have documented this misconception.
 Trowbridge, D. E. and McDermott, L. C. () Investigation of student understanding of the concept of acceleration in one dimension. American Journal of Physics, 49 (3),
242253.
A sample of 35 undergraduate students from the University of Washington were asked to complete four motionbased tasks (developed from work by Jean Piaget) during the course of a 2030 minute interview. 28 students were from a calculus physics course, and 7 were from an academically disadvantaged class. Several types of conceptual difficulties were identified, and it was determined that "fewer than half of the students demonstrated sufficient qualitative understanding of acceleration as a ratio to be able to apply this concept in a real situation."
 Saltiel, E. and Malgrange, J. L. () 'Spontaneous' ways of reasoning in elementary kinematics. European Journal of Physics, 1 (2),
7380.
The aim of this study was to explore and analyse 'spontaneous' ways of reasoning (SWR) of students in elementary kinematics (uniform motion in galilean frames). A set of experiments presented to 80 elevenyearold children and to some 700 first and fourthyear university students showed types of right and wrong answer which varied little from one sample of pupils to another. It seems difficult to attribute these results solely to school learning; but they can be well accounted for if the authors assume the existence of an organised system which the authors call the 'natural model', as opposed to the kinematic model of the physicists. This model involves two components which always interact: a purely descriptive one describing motion, and a causal one explaining motion.