Test your understanding of acceleration as a vector quantity in two dimensions. This medium-level quiz covers velocity changes, acceleration components, and why an object can accelerate even when its speed remains constant.
Q1. What does acceleration measure?
Acceleration is the rate at which velocity changes with time. Since velocity is a vector, that change can involve speed, direction, or both.
Q2. Why is acceleration a vector quantity?
Acceleration inherits vector status because it describes the change in velocity, which has both magnitude and direction.
Q3. A velocity changes from ##(2,1)\ \text{m/s}## to ##(8,5)\ \text{m/s}## in ##2\ \text{s}##. What is the average acceleration?
The velocity change is ##(8-2,5-1)=(6,4)\ \text{m/s}##. Dividing each component by ##2\ \text{s}## gives ##(3,2)\ \text{m/s}^2##.
Q4. How is the horizontal component of average acceleration found over a time interval?
The horizontal acceleration component is the horizontal velocity change divided by the time interval: ##a_{x,\text{avg}}=\dfrac{\Delta v_x}{\Delta t}##.
Q5. In a velocity-vector diagram, which direction does average acceleration point?
Average acceleration points in the direction of ##\Delta\vec{v}##, the difference between the final and initial velocity vectors.
Q6. A car travels around a bend at constant speed. What can be concluded about its acceleration?
Velocity changes when its direction changes, even if its magnitude, or speed, stays constant. Therefore, the car accelerates around the bend.
Q7. An object’s speed stays constant while its direction changes. Which statement is correct?
Velocity includes direction as well as speed. A direction change is a velocity change and therefore indicates acceleration.
Q8. What does instantaneous acceleration describe?
Instantaneous acceleration describes how rapidly velocity is changing at a specific instant, rather than across a whole interval.
Q9. What is the SI unit of acceleration?
Acceleration is velocity change per unit time. Since velocity is measured in ##\text{m/s}##, acceleration is measured in ##\text{m/s}^2##.
Q10. If acceleration is perpendicular to velocity, what is its immediate effect in the lesson’s description?
Perpendicular acceleration bends the path by changing velocity’s direction without altering its magnitude, the speed.
Q11. Which description correctly distinguishes tangential and normal acceleration?
Tangential acceleration is associated with changing speed, while normal acceleration is associated with changing the direction of velocity.
Q12. At the apex of a ball’s flight, its vertical velocity is momentarily zero. What does this fact alone tell us about its acceleration?
Velocity and acceleration are different quantities. The fact that one velocity component is momentarily zero does not establish that acceleration is zero.
Q13. A body’s velocity changes from ##(4,3)\ \text{m/s}## to ##(4,9)\ \text{m/s}## in ##3\ \text{s}##. What is its average acceleration?
The horizontal velocity does not change, while the vertical velocity changes by ##6\ \text{m/s}##. Dividing the component changes by ##3\ \text{s}## gives ##(0,2)\ \text{m/s}^2##.
Q14. An object’s velocity changes by ##(0,-6)\ \text{m/s}## over ##3\ \text{s}##. What is its average acceleration?
Average acceleration is the velocity change divided by elapsed time. Thus ##(0,-6)/3=(0,-2)\ \text{m/s}^2##.
Q15. If an object’s velocity vector remains unchanged over a time interval, what is its average acceleration for that interval?
If the velocity vector is unchanged, its change is zero. Dividing that zero change by the time interval gives zero average acceleration.
Q16. A velocity triangle is used to compare an object’s initial and final velocities. Which vector represents the change in velocity?
With the velocity vectors’ tails aligned, the change-in-velocity vector runs from the tip of the initial vector to the tip of the final vector.
Q17. Which example best shows that acceleration does not always mean speeding up or slowing down?
A car rounding a bend at constant speed changes its velocity direction. That change means it accelerates even though its speed does not change.
Q18. Why is the statement “the object accelerates at ##5\ \text{m/s}^2##” incomplete as a full vector description?
A complete vector description includes both magnitude and direction. The statement gives an acceleration magnitude but does not specify its direction.
Q19. An object has a nonzero horizontal velocity change but no vertical velocity change during an interval. What can be said about its average acceleration components?
Each average acceleration component equals the corresponding velocity change divided by the same elapsed time. A nonzero horizontal change and zero vertical change therefore give a nonzero horizontal component and zero vertical component.
Q20. Why can a two-dimensional acceleration problem be resolved into horizontal and vertical components?
Because velocity is a vector, its change can be resolved into components. Each acceleration component follows from the corresponding velocity change over the time interval.