Q.Can the direction of the velocity of an object moving in a straight line be different from the direction of its acceleration? Explain with an example.

[!TLDR] Yes — velocity and acceleration can point in opposite directions, as in a ball thrown upward (velocity up, acceleration due to gravity always down). [!ANSWER] Yes; example: a ball thrown vertically upward has its velocity directed upward while its acceleration (g) is directed downward throughout the ascent.

Yes, velocity and acceleration can point in different, even exactly opposite, directions. They are independent vector quantities along the line of motion; nothing requires them to be aligned.

Example. Take a ball thrown vertically upward. While it is rising, its velocity is directed upward. Its acceleration, however, is due to gravity alone, which always acts downward, throughout the entire flight — during the ascent, at the highest point, and during the subsequent descent. During the upward journey, therefore, velocity (up) and acceleration (down) are in exactly opposite directions; this is precisely what produces the deceleration (retardation, Section 2.5) that eventually brings the ball's upward velocity to zero at the highest point.

Contrast with the descent. Once the ball starts falling, its velocity is now directed downward, the same direction as the (unchanged) downward acceleration due to gravity — so during the descent, velocity and acceleration point in the same direction, and the ball's speed increases. The acceleration itself, notably, never changes throughout the flight (it is $g$, downward, at every instant); only its relationship to the instantaneous velocity direction changes between the two phases.

General rule. Whenever a body decelerates (Section 2.5), its acceleration is, by definition, opposite to its instantaneous velocity; whenever it accelerates (speeds up) in the ordinary sense, acceleration and velocity point the same way.

[!ANSWER] Yes — during the upward flight of a vertically thrown ball, velocity points upward while acceleration (due to gravity) points downward, showing the two can be in opposite directions.

Use the vertical-throw example, tracking velocity direction versus the constant downward direction of gravitational acceleration through the rising and falling phases.

• Assuming acceleration must always point the same way as velocity
• Forgetting that gravity's direction (and hence the acceleration) never changes during the throw, only the velocity direction does
• Giving an example where the body is not actually accelerating at all