Question

Which of the following situations is possible?

An object can have acceleration, but constant velocity.
The velocity of an object may be zero but acceleration is not zero.
Distance and the magnitude of displacement are equal in circular motion.
Average speed and the magnitude of average velocity are always equal in circular motion.

Answer 1

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(a)

Let say a stone is thrown in vertical direction with initial speed u. As the time passes its velocity decreases and at the maximum height it attained, its velocity is zero but it has an acceleration (9.8)m/s

2

in the downward direction due to gravity.

(b)

When a pebble is tied with an end of string and it is whirled in horizontal circular motion with the other end of the string at the centre of circular path, then it has a constant magnitude of centripetal acceleration towards the centre. Hence the acceleration is in perpendicular direction to the motion of pebble.

Answer 2

The velocity of an object  may be zero but acceleration is not zero. This is a possible situation.

Explanation:

• Acceleration is the rate of change of velocity with time.

• Acceleration roughly means “change in velocity.” If this change in velocity is consistent in only one direction, the body will reach a point at which its velocity is zero.

Examples:

1. A car stops at red light and while the light turns green, it has to accelerate. Now, because it started stationary, there is a point at which velocity of car was zero and acceleration was nonzero. If acceleration had to be zero when the velocity of the car is zero, the car wouldn't be able to move.
2. When a basketball is dropped onto the pavement, ball falls and hits the ground and comes back up. Because its direction of motion changed, its velocity must have been zero at some point during the bounce. But the acceleration is always acting on it.

• An object cannot have acceleration but constant velocity. Acceleration is defined as change in velocity. So, either the magnitude or the direction of velocity has to change for acceleration to exist.
• Distance and magnitude of displacement is not equal in a circular motion because when a body is motion in circular motion, the total path covered (which is distance) by the body is always greater than the straight line between its initial and final position (which is displacement).
• Average speed and the magnitude of average velocity are not always equal in circular motion, because the distance and displacement is not same.