Physics · Motion In A Straight Line · NEET
It is displacement divided by time: v_avg = Delta_x / Delta_t. Displacement is the straight-line change in position (final minus initial), not the length of the path. That is exactly why average velocity is a vector while average speed (distance/time) is a scalar. NEET loves to swap these two, so always ask: did they give displacement or path length?
Because displacement is (final position - initial position). If an object goes out and comes back to the same point, Delta_x = 0, so v_avg = 0 / t = 0, no matter how far it actually travelled. Its average speed is not zero because distance covered is not zero. Round trips are the classic zero-average-velocity case in NEET.
Yes. In one dimension you first fix a positive direction (a sign convention). If the final position is on the negative side of the initial position, Delta_x is negative, so v_avg is negative. A negative sign only tells you the direction of net motion, not that motion was slow. Average speed can never be negative.
Average velocity between two instants is the slope of the straight line (the chord) joining those two points on the x-t graph: v_avg = (x2 - x1)/(t2 - t1). It is the slope of the secant line, not the tangent. The tangent slope gives instantaneous velocity instead.
No. It depends only on the initial and final positions and the total time. Two objects that start and end at the same points in the same time have the same average velocity even if one took a longer, more winding route. Only average speed depends on the actual path length.
A toy car with charge q moves on a frictionless horizontal plane under a uniform electric field E. Due to the force qE, its velocity increases from 0 to 6 m/s in one second. At that instant the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between 0 to 3 seconds are respectively:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
v_avg = Delta_x / Delta_t = (x2 - x1) / (t2 - t1), where x2 - x1 is the displacement and t2 - t1 is the time interval. Its SI unit is m/s and it is a vector quantity.
Average velocity = displacement / time (a vector, can be negative or zero). Average speed = total distance / time (a scalar, always non-negative). For a straight-line trip without reversing direction, their magnitudes are equal; otherwise average speed is greater.
Only for uniform (constant) acceleration. Then average velocity = (u + v)/2, where u and v are the initial and final velocities. For non-uniform acceleration you must use displacement / time instead.
It is a vector because it is defined using displacement, which has both magnitude and direction. In one dimension its direction is shown by a + or - sign based on your chosen sign convention.
The slope of the chord joining two points on an x-t graph gives the average velocity between those instants; the slope of the tangent at a point gives the instantaneous velocity.
