A car travels forward with constant velocity. It goes over a small stone, which gets stuck in the groove of a tire. The initial acceleration of the stone, as it leaves the surface of the road is,

Question

a)vertically up
b)horizontally forward
c)horizontally backwards
d) zero
e)greater than zero but less than 45 degrees below the horizontal

I think the answer would be d)zero since the car's tire is going at constant velocity. Would my thinking be correct?

The correct answer is "vertically up". The car's tire is going at constant speed, but the velocity is constantly changing direction. The instantaneous velocity of the part of the tire that is in contact with the road is zero, so the stone is not subjected to a tangential acceleration.

From the moment it is caught in the tire it is rotating with the tire. An object that is rotating around some point with constant speed is accelerating toward that point with the centripetal acceleration of v^2/r.

Answer 1

A vertically upward since that is the direction of centripetal acceleration at that time.

Answer 2

A car traveling in a straight line has a velocity
of +4.4 m/s. After an acceleration of 0.65
m/s2
, the car’s velocity is +8.8 m/s.
In what time interval did the acceleration
occur?

Answer 3

the acceleration is upward, but it's not due to centripetal acceleration because it's velocity is zero as it stuck in the tire. As the tire moves forward, you can draw a series pictures to show that the stone is moving upward.