An object's velocity and acceleration have the same sign. What is happening to its speed?
You've already seen the rule: an object speeds up when its velocity and acceleration have the same sign and slows down when they have opposite signs. Now use it on real motions.
To decide, write down two signs: the velocity's and the acceleration's.
A ball has v = −8 m/s and a = −2 m/s². Velocity negative, acceleration negative. The signs match, so the ball is speeding up.
A car on a highway has v = +12 m/s and a = −3 m/s². Is it speeding up or slowing down?
Write down the two signs:
velocity: positive
acceleration: negative
Compare the signs:
opposite signs
The car is slowing down, because an object speeds up when its velocity and acceleration have the same sign and slows down when they have opposite signs.
A freight elevator has v = +3 m/s and a = +1.5 m/s². Is it speeding up or slowing down?
A skateboarder has v = +9 m/s and a = +4 m/s². Is she speeding up or slowing down?
Write down the two signs:
velocity: positive
acceleration: positive
Compare the signs:
the same sign
She is speeding up: her velocity and acceleration have the same sign.
A luggage cart rolls with v = -6 m/s while its acceleration is +2 m/s². Is it speeding up or slowing down?
A downhill skier has v = -10 m/s and a = -4 m/s². Is she speeding up or slowing down?
A delivery van has v = +20 m/s at the moment its acceleration becomes -4 m/s². From that moment, is the van speeding up or slowing down?
A kayak drifts in the negative direction at 3 m/s while the wind gives it an acceleration of 1 m/s² pointing in the positive direction. Is the kayak speeding up or slowing down?
Sled A has v = -12 m/s and a = -3 m/s². Sled B has v = +12 m/s and a = -3 m/s². Which sled is speeding up?