A) An object moves in a straight line at constant speed.
B) An object moves with uniform circular motion.
C) An object travels as a projectile in a gravitational field with negligible air resistance.
In which of the situations would the object be accelerated?
1. All exhibit acceleration.
2. None exhibits acceleration.
3. C only
4. A and B only
5. A only
6. B only
7. A and C only
8. B and C only
By DEFINITION the acceleration a VECTOR is equal to the first derivative (with respect to the time) of the VECTOR v speed. In other words the acceleration is equal to the changes per unity of time of the VECTOR speed.
Since in the constant linear motion there is no change whatsoever of the vector speed there is no acceleration.
Since in the case of the circular motion the speed vector rotates over time there is centripetal acceleration (not zero!)
Since in the case of moving in a gravitational filed there is gravitational acceleration g exerted on the object the acceleration in this case is not zero (in other words the trajectory is parabolic and the speed vector changes).
Therefore the correct answer is 8. B) and C) only.